Publisher: Cambridge University Press   (Total: 386 journals)

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Showing 1 - 200 of 386 Journals sorted alphabetically
Acta Neuropsychiatrica     Hybrid Journal   (Followers: 6, SJR: 0.733, CiteScore: 2)
Acta Numerica     Hybrid Journal   (Followers: 5, SJR: 6.709, CiteScore: 10)
Advances in Animal Biosciences     Full-text available via subscription   (Followers: 14)
Advances in Applied Mathematics and Mechanics     Full-text available via subscription   (Followers: 2, SJR: 0.441, CiteScore: 1)
Aeronautical J., The     Hybrid Journal   (Followers: 7)
Africa     Hybrid Journal   (Followers: 24, SJR: 0.582, CiteScore: 1)
African Studies Review     Full-text available via subscription   (Followers: 21, SJR: 0.437, CiteScore: 1)
Ageing & Society     Hybrid Journal   (Followers: 43, SJR: 0.756, CiteScore: 2)
Agricultural and Resource Economics Review     Open Access   (Followers: 7, SJR: 0.414, CiteScore: 1)
AI EDAM     Hybrid Journal   (Followers: 2, SJR: 0.375, CiteScore: 1)
AJIL Unbound     Open Access  
AJS Review     Full-text available via subscription   (Followers: 4, SJR: 0.128, CiteScore: 0)
American Political Science Review     Hybrid Journal   (Followers: 340, SJR: 5.587, CiteScore: 4)
Anatolian Studies     Full-text available via subscription   (Followers: 5, SJR: 0.528, CiteScore: 1)
Ancient Mesoamerica     Hybrid Journal   (Followers: 12, SJR: 0.478, CiteScore: 1)
Anglo-Saxon England     Hybrid Journal   (Followers: 36, SJR: 0.1, CiteScore: 0)
animal     Hybrid Journal   (Followers: 4, SJR: 0.842, CiteScore: 2)
Animal Health Research Reviews     Hybrid Journal   (Followers: 3, SJR: 0.69, CiteScore: 2)
Animal Science     Full-text available via subscription   (Followers: 10)
Annals of Actuarial Science     Full-text available via subscription   (Followers: 1)
Annual of the British School at Athens     Full-text available via subscription   (Followers: 16, SJR: 0.177, CiteScore: 0)
Annual Review of Applied Linguistics     Hybrid Journal   (Followers: 45, SJR: 3.223, CiteScore: 4)
Antarctic Science     Hybrid Journal   (Followers: 1, SJR: 0.643, CiteScore: 1)
Antichthon     Full-text available via subscription   (Followers: 3, SJR: 0.101, CiteScore: 0)
Antiquaries J., The     Full-text available via subscription   (Followers: 11, SJR: 0.106, CiteScore: 0)
Antiquity     Hybrid Journal   (Followers: 33)
ANZIAM J.     Open Access   (Followers: 1, SJR: 0.216, CiteScore: 0)
Applied Psycholinguistics     Hybrid Journal   (Followers: 25, SJR: 0.945, CiteScore: 2)
APSIPA Transactions on Signal and Information Processing     Open Access   (Followers: 9, SJR: 0.404, CiteScore: 2)
Arabic Sciences and Philosophy     Hybrid Journal   (Followers: 9, SJR: 0.101, CiteScore: 0)
Arbor Clinical Nutrition Updates     Full-text available via subscription   (Followers: 5)
Archaeological Dialogues     Hybrid Journal   (Followers: 35, SJR: 0.898, CiteScore: 1)
Archaeological Reports     Full-text available via subscription   (Followers: 5, SJR: 0.128, CiteScore: 0)
Architectural History     Full-text available via subscription  
arq: Architectural Research Quarterly     Hybrid Journal   (Followers: 7, SJR: 0.123, CiteScore: 0)
Art Libraries J.     Full-text available via subscription   (Followers: 1)
Asian J. of Comparative Law     Hybrid Journal   (Followers: 11, SJR: 0.129, CiteScore: 0)
Asian J. of Intl. Law     Hybrid Journal   (Followers: 17, SJR: 0.135, CiteScore: 0)
Asian J. of Law and Society     Hybrid Journal   (Followers: 7, SJR: 0.195, CiteScore: 0)
Astin Bulletin     Full-text available via subscription   (Followers: 1, SJR: 0.878, CiteScore: 1)
Australasian J. of Organisational Psychology     Hybrid Journal   (Followers: 9, SJR: 0.154, CiteScore: 1)
Australian J. of Environmental Education     Full-text available via subscription   (Followers: 9, SJR: 0.403, CiteScore: 1)
Australian J. of Indigenous Education, The     Full-text available via subscription   (Followers: 11, SJR: 0.26, CiteScore: 1)
Australian J. of Rehabilitation Counseling     Full-text available via subscription   (Followers: 6, SJR: 0.144, CiteScore: 0)
Austrian History Yearbook     Full-text available via subscription   (Followers: 11, SJR: 0.161, CiteScore: 0)
Behavioral and Brain Sciences     Hybrid Journal   (Followers: 38, SJR: 0.595, CiteScore: 1)
Behaviour Change     Full-text available via subscription   (Followers: 13, SJR: 0.508, CiteScore: 1)
Behavioural and Cognitive Psychotherapy     Hybrid Journal   (Followers: 187, SJR: 0.976, CiteScore: 2)
Bilingualism: Language and Cognition     Hybrid Journal   (Followers: 45, SJR: 1.446, CiteScore: 2)
Biofilms     Full-text available via subscription   (Followers: 2)
Bird Conservation Intl.     Hybrid Journal   (Followers: 25, SJR: 0.581, CiteScore: 1)
BJPsych Advances     Full-text available via subscription   (Followers: 57, SJR: 0.275, CiteScore: 0)
BJPsych Intl.     Open Access   (Followers: 2)
BJPsych Open     Open Access   (Followers: 3)
Brain Impairment     Full-text available via subscription   (Followers: 2, SJR: 0.321, CiteScore: 1)
Breast Cancer Online     Full-text available via subscription   (Followers: 6)
Britannia     Full-text available via subscription   (Followers: 11, SJR: 0.111, CiteScore: 0)
British Actuarial J.     Full-text available via subscription  
British Catholic History     Hybrid Journal   (Followers: 2, SJR: 0.133, CiteScore: 1)
British J. for the History of Science     Hybrid Journal   (Followers: 25, SJR: 0.235, CiteScore: 0)
British J. of Anaesthetic and Recovery Nursing     Full-text available via subscription   (Followers: 8)
British J. of Music Education     Hybrid Journal   (Followers: 24, SJR: 0.564, CiteScore: 1)
British J. Of Nutrition     Hybrid Journal   (Followers: 95, SJR: 1.612, CiteScore: 4)
British J. of Political Science     Hybrid Journal   (Followers: 229, SJR: 4.661, CiteScore: 4)
British J. of Psychiatry     Hybrid Journal   (Followers: 241, SJR: 2.844, CiteScore: 3)
Bulletin of Entomological Research     Hybrid Journal   (Followers: 13, SJR: 0.805, CiteScore: 2)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2, SJR: 0.555, CiteScore: 1)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2, SJR: 0.44, CiteScore: 0)
Bulletin of the School of Oriental and African Studies     Hybrid Journal   (Followers: 21, SJR: 0.146, CiteScore: 0)
Business and Human Rights J.     Full-text available via subscription   (Followers: 4, SJR: 0.536, CiteScore: 1)
Business Ethics Quarterly     Full-text available via subscription   (Followers: 18, SJR: 1.098, CiteScore: 2)
Business History Review     Hybrid Journal   (Followers: 16, SJR: 0.347, CiteScore: 1)
Cambridge Archaeological J.     Hybrid Journal   (Followers: 165, SJR: 1.121, CiteScore: 1)
Cambridge Classical J.     Full-text available via subscription   (Followers: 24, SJR: 0.101, CiteScore: 0)
Cambridge J. of Postcolonial Literary Inquiry     Hybrid Journal   (Followers: 7)
Cambridge Law J.     Hybrid Journal   (Followers: 217, SJR: 0.213, CiteScore: 0)
Cambridge Opera J.     Hybrid Journal   (Followers: 4, SJR: 0.14, CiteScore: 0)
Cambridge Quarterly of Healthcare Ethics     Hybrid Journal   (Followers: 12, SJR: 0.299, CiteScore: 1)
Cambridge Yearbook of European Legal Studies     Full-text available via subscription  
Camden Fifth Series     Full-text available via subscription   (Followers: 3)
Canadian Entomologist     Hybrid Journal   (Followers: 5, SJR: 0.482, CiteScore: 1)
Canadian J. of Emergency Medicine     Hybrid Journal   (Followers: 13, SJR: 0.624, CiteScore: 1)
Canadian J. of Law & Jurisprudence     Full-text available via subscription   (Followers: 9, SJR: 0.237, CiteScore: 0)
Canadian J. of Law and Society     Hybrid Journal   (Followers: 21, SJR: 0.259, CiteScore: 1)
Canadian J. of Mathematics / J. canadien de mathématiques     Hybrid Journal  
Canadian J. of Neurological Sciences     Full-text available via subscription   (SJR: 0.549, CiteScore: 1)
Canadian J. of Political Science/Revue canadienne de science politique     Full-text available via subscription   (Followers: 25, SJR: 0.385, CiteScore: 1)
Canadian J. on Aging     Hybrid Journal   (Followers: 14, SJR: 0.426, CiteScore: 1)
Canadian Mathematical Bulletin     Hybrid Journal  
Canadian Yearbook of Intl. Law / Annuaire canadien de droit international     Full-text available via subscription   (Followers: 3)
Cardiology in the Young     Hybrid Journal   (Followers: 34, SJR: 0.372, CiteScore: 1)
Central European History     Full-text available via subscription   (Followers: 33, SJR: 0.159, CiteScore: 0)
Children Australia     Partially Free   (Followers: 2, SJR: 0.255, CiteScore: 0)
China Quarterly     Hybrid Journal   (Followers: 54, SJR: 2.289, CiteScore: 3)
Chinese J. of Agricultural Biotechnology     Full-text available via subscription   (Followers: 4)
Church History : Studies in Christianity and Culture     Full-text available via subscription   (Followers: 77, SJR: 0.106, CiteScore: 0)
Classical Quarterly     Full-text available via subscription   (Followers: 36, SJR: 0.204, CiteScore: 0)
Classical Review     Full-text available via subscription   (Followers: 29)
CNS Spectrums     Hybrid Journal   (Followers: 3, SJR: 1.391, CiteScore: 3)
Cognitive Behaviour Therapist     Hybrid Journal   (Followers: 14)
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4, SJR: 0.839, CiteScore: 1)
Communications in Computational Physics     Full-text available via subscription   (Followers: 3, SJR: 1.048, CiteScore: 2)
Comparative Studies in Society and History     Full-text available via subscription   (Followers: 50, SJR: 0.585, CiteScore: 1)
Compositio Mathematica     Full-text available via subscription   (SJR: 3.139, CiteScore: 1)
Contemporary European History     Hybrid Journal   (Followers: 36, SJR: 0.263, CiteScore: 1)
Continuity and Change     Hybrid Journal   (Followers: 12, SJR: 0.107, CiteScore: 0)
Dance Research J.     Full-text available via subscription   (Followers: 17, SJR: 0.211, CiteScore: 0)
Development and Psychopathology     Hybrid Journal   (Followers: 10, SJR: 2.068, CiteScore: 4)
Dialogue Canadian Philosophical Review/Revue canadienne de philosophie     Full-text available via subscription   (Followers: 5, SJR: 0.156, CiteScore: 0)
Diamond Light Source Proceedings     Full-text available via subscription   (Followers: 1)
Disaster Medicine and Public Health Preparedness     Hybrid Journal   (Followers: 15, SJR: 0.471, CiteScore: 1)
Du Bois Review: Social Science Research on Race     Full-text available via subscription   (Followers: 10, SJR: 0.561, CiteScore: 1)
Early China     Hybrid Journal   (Followers: 3)
Early Music History     Hybrid Journal   (Followers: 9, SJR: 0.101, CiteScore: 0)
Earth and Environmental Science Transactions of the Royal Society of Edinburgh     Hybrid Journal   (Followers: 5)
East Asian J. on Applied Mathematics     Full-text available via subscription   (SJR: 0.418, CiteScore: 1)
Ecclesiastical Law J.     Full-text available via subscription   (Followers: 6, SJR: 0.114, CiteScore: 0)
Econometric Theory     Hybrid Journal   (Followers: 20, SJR: 2.915, CiteScore: 1)
Economics and Philosophy     Hybrid Journal   (Followers: 19, SJR: 0.622, CiteScore: 1)
Edinburgh J. of Botany     Hybrid Journal   (SJR: 0.283, CiteScore: 1)
Educational and Developmental Psychologist     Full-text available via subscription   (Followers: 10, SJR: 0.146, CiteScore: 0)
Eighteenth-Century Music     Hybrid Journal   (Followers: 15, SJR: 0.113, CiteScore: 0)
English Language and Linguistics     Hybrid Journal   (Followers: 24, SJR: 0.52, CiteScore: 1)
English Profile J.     Hybrid Journal   (Followers: 2)
English Today     Hybrid Journal   (Followers: 13, SJR: 0.279, CiteScore: 0)
Enterprise & Society : The Intl. J. of Business History     Hybrid Journal   (Followers: 18, SJR: 0.245, CiteScore: 1)
Environment and Development Economics     Hybrid Journal   (Followers: 39, SJR: 0.617, CiteScore: 1)
Environmental Conservation     Hybrid Journal   (Followers: 60, SJR: 1.028, CiteScore: 2)
Environmental Practice     Full-text available via subscription   (Followers: 3, SJR: 0.145, CiteScore: 0)
Epidemiology & Infection     Hybrid Journal   (Followers: 22, SJR: 1.128, CiteScore: 2)
Epidemiology and Psychiatric Sciences     Hybrid Journal   (Followers: 3, SJR: 1.494, CiteScore: 2)
Episteme     Hybrid Journal   (Followers: 12, SJR: 0.756, CiteScore: 1)
Ergodic Theory and Dynamical Systems     Hybrid Journal   (Followers: 2, SJR: 1.193, CiteScore: 1)
Ethics & Intl. Affairs     Full-text available via subscription   (Followers: 17, SJR: 0.557, CiteScore: 1)
European Constitutional Law Review (EuConst)     Full-text available via subscription   (Followers: 36, SJR: 1.009, CiteScore: 1)
European J. of Applied Mathematics     Hybrid Journal   (SJR: 0.52, CiteScore: 1)
European J. of Intl. Security     Hybrid Journal   (Followers: 1)
European J. of Sociology     Hybrid Journal   (Followers: 37, SJR: 0.643, CiteScore: 1)
European Political Science Review     Hybrid Journal   (Followers: 27, SJR: 1.816, CiteScore: 2)
European Review     Hybrid Journal   (Followers: 19, SJR: 0.131, CiteScore: 0)
Evolutionary Human Sciences     Open Access   (Followers: 1)
Experimental Agriculture     Hybrid Journal   (Followers: 14, SJR: 0.542, CiteScore: 1)
Expert Reviews in Molecular Medicine     Hybrid Journal   (Followers: 1, SJR: 1.647, CiteScore: 4)
Fetal and Maternal Medicine Review     Hybrid Journal   (Followers: 6)
Financial History Review     Full-text available via subscription   (Followers: 15, SJR: 0.238, CiteScore: 1)
Foreign Policy Bulletin     Hybrid Journal   (Followers: 6)
Forum of Mathematics, Pi     Open Access   (Followers: 1)
Forum of Mathematics, Sigma     Open Access   (Followers: 1)
Genetics Research     Hybrid Journal   (Followers: 4, SJR: 0.483, CiteScore: 1)
Geological Magazine     Hybrid Journal   (Followers: 16, SJR: 0.966, CiteScore: 2)
Glasgow Mathematical J.     Full-text available via subscription   (SJR: 0.604, CiteScore: 0)
Global Constitutionalism     Hybrid Journal   (Followers: 17)
Global Mental Health     Open Access   (Followers: 9)
Global Sustainability     Open Access   (Followers: 1)
Government and Opposition     Full-text available via subscription   (Followers: 24, SJR: 0.965, CiteScore: 2)
Greece & Rome     Partially Free   (Followers: 30, SJR: 0.113, CiteScore: 0)
Hague J. on the Rule of Law     Full-text available via subscription   (Followers: 14, SJR: 0.271, CiteScore: 1)
Harvard Theological Review     Full-text available via subscription   (Followers: 78, SJR: 0.165, CiteScore: 0)
Health Economics, Policy and Law     Hybrid Journal   (Followers: 29, SJR: 0.745, CiteScore: 1)
Hegel Bulletin     Full-text available via subscription   (Followers: 2)
High Power Laser Science and Engineering     Open Access   (Followers: 4, SJR: 0.901, CiteScore: 3)
Historical J.     Hybrid Journal   (Followers: 42, SJR: 0.247, CiteScore: 1)
History in Africa     Full-text available via subscription   (Followers: 9)
Horizons     Partially Free   (Followers: 1, SJR: 0.129, CiteScore: 0)
Industrial and Organizational Psychology     Hybrid Journal   (Followers: 27, SJR: 0.916, CiteScore: 1)
Infection Control and Hospital Epidemiology     Full-text available via subscription   (Followers: 49, SJR: 1.97, CiteScore: 3)
Intl. & Comparative Law Quarterly     Full-text available via subscription   (Followers: 261, SJR: 0.369, CiteScore: 1)
Intl. Annals of Criminology     Full-text available via subscription  
Intl. J. of Asian Studies     Hybrid Journal   (Followers: 13, SJR: 0.143, CiteScore: 0)
Intl. J. of Astrobiology     Hybrid Journal   (Followers: 4, SJR: 0.548, CiteScore: 1)
Intl. J. of Cultural Property     Full-text available via subscription   (Followers: 14, SJR: 0.253, CiteScore: 1)
Intl. J. of Disability Management Research     Full-text available via subscription   (Followers: 9, SJR: 0.105, CiteScore: 0)
Intl. J. of Law in Context     Hybrid Journal   (Followers: 17, SJR: 0.275, CiteScore: 1)
Intl. J. of Legal Information     Full-text available via subscription   (Followers: 345)
Intl. J. of Microwave and Wireless Technologies     Hybrid Journal   (Followers: 10, SJR: 0.184, CiteScore: 1)
Intl. J. of Middle East Studies     Hybrid Journal   (Followers: 72, SJR: 0.434, CiteScore: 0)
Intl. J. of Technology Assessment in Health Care     Hybrid Journal   (Followers: 14, SJR: 0.714, CiteScore: 1)
Intl. Labor and Working-Class History     Full-text available via subscription   (Followers: 14, SJR: 0.182, CiteScore: 0)
Intl. Organization     Full-text available via subscription   (Followers: 108, SJR: 8.527, CiteScore: 5)
Intl. Psychogeriatrics     Hybrid Journal   (Followers: 12, SJR: 1.048, CiteScore: 2)
Intl. Review of Social History     Full-text available via subscription   (Followers: 29, SJR: 0.315, CiteScore: 1)
Intl. Review of the Red Cross     Full-text available via subscription   (Followers: 12, SJR: 0.214, CiteScore: 0)
Intl. Theory: A J. of Intl. Politics, Law and Philosophy     Hybrid Journal   (Followers: 19, SJR: 2.293, CiteScore: 2)
Iraq     Full-text available via subscription   (Followers: 5)
Irish Historical Studies     Hybrid Journal   (Followers: 7, SJR: 0.103, CiteScore: 0)
Irish J. of Psychological Medicine     Hybrid Journal   (Followers: 2, SJR: 0.221, CiteScore: 0)
Israel Law Review     Hybrid Journal   (Followers: 2, SJR: 0.165, CiteScore: 0)
Italian Political Science Review / Rivista Italiana di Scienza Politica     Hybrid Journal   (Followers: 1)
Itinerario     Full-text available via subscription   (Followers: 11, SJR: 0.158, CiteScore: 0)
J. of African History     Hybrid Journal   (Followers: 23, SJR: 0.348, CiteScore: 1)
J. of African Law     Full-text available via subscription   (Followers: 3, SJR: 0.113, CiteScore: 0)
J. of Agricultural and Applied Economics     Open Access   (Followers: 4, SJR: 0.263, CiteScore: 1)
J. of Agricultural Science     Full-text available via subscription   (Followers: 8, SJR: 0.563, CiteScore: 1)
J. of American Studies     Hybrid Journal   (Followers: 21, SJR: 0.164, CiteScore: 0)
J. of Anglican Studies     Hybrid Journal   (Followers: 8, SJR: 0.101, CiteScore: 0)
J. of Applied Animal Nutrition     Hybrid Journal   (Followers: 4)
J. of Asian Studies     Full-text available via subscription   (Followers: 42, SJR: 0.591, CiteScore: 1)
J. of Benefit-Cost Analysis     Hybrid Journal   (Followers: 4)
J. of Biosocial Science     Hybrid Journal   (Followers: 5, SJR: 0.48, CiteScore: 1)
J. of British Studies     Full-text available via subscription   (Followers: 34, SJR: 0.246, CiteScore: 0)

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Forum of Mathematics, Pi
Number of Followers: 1  

  This is an Open Access Journal Open Access journal
ISSN (Online) 2050-5086
Published by Cambridge University Press Homepage  [386 journals]
  • SERRE WEIGHTS AND BREUIL’S LATTICE CONJECTURE IN DIMENSION THREE

    • Authors: DANIEL LE; BAO V. LE HUNG, BRANDON LEVIN, STEFANO MORRA
      Abstract: We prove in generic situations that the lattice in a tame type induced by the completed cohomology of a $U(3)$ -arithmetic manifold is purely local, that is, only depends on the Galois representation at places above $p$ . This is a generalization to $\text{GL}_{3}$ of the lattice conjecture of Breuil. In the process, we also prove the geometric Breuil–Mézard conjecture for (tamely) potentially crystalline deformation rings with Hodge–Tate weights $(2,1,0)$ as well as the Serre weight conjectures of Herzig [‘The weight in a Serre-type conjecture for tame $n$ -dimensional Galois representations’, Duke Math. J. 149(1) (2009), 37–116] over an unramified field extending the results of Le et al. [‘Potentially crystalline deformation 3985 rings and Serre weight conjectures: shapes and shadows’, Invent. Math. 212(1) (2018), 1–107]. We also prove results in modular representation theory about lattices in Deligne–Lusztig representations for the group $\text{GL}_{3}(\mathbb{F}_{q})$ .
      PubDate: 2020-03-25T00:00:00.000Z
      DOI: 10.1017/fmp.2020.1
      Issue No: Vol. 8 (2020)
       
  • ENUMERATION OF MEANDERS AND MASUR–VEECH VOLUMES

    • Authors: VINCENT DELECROIX; ÉLISE GOUJARD, PETER ZOGRAF, ANTON ZORICH
      Abstract: A meander is a topological configuration of a line and a simple closed curve in the plane (or a pair of simple closed curves on the 2-sphere) intersecting transversally. Meanders can be traced back to H. Poincaré and naturally appear in various areas of mathematics, theoretical physics and computational biology (in particular, they provide a model of polymer folding). Enumeration of meanders is an important open problem. The number of meanders with $2N$ crossings grows exponentially when $N$ grows, but the long-standing problem on the precise asymptotics is still out of reach.We show that the situation becomes more tractable if one additionally fixes the topological type (or the total number of minimal arcs) of a meander. Then we are able to derive simple asymptotic formulas for the numbers of meanders as $N$ tends to infinity. We also compute the asymptotic probability of getting a simple closed curve on a sphere by identifying the endpoints of two arc systems (one on each of the two hemispheres) along the common equator.The new tools we bring to bear are based on interpretation of meanders as square-tiled surfaces with one horizontal and one vertical cylinder. The proofs combine recent results on Masur–Veech volumes of moduli spaces of meromorphic quadratic differentials in genus zero with our new observation that horizontal and vertical separatrix diagrams of integer quadratic differentials are asymptotically uncorrelated. The additional combinatorial constraints we impose in this article yield explicit polynomial asymptotics.
      PubDate: 2020-03-23T00:00:00.000Z
      DOI: 10.1017/fmp.2020.2
      Issue No: Vol. 8 (2020)
       
  • PRIMES REPRESENTED BY INCOMPLETE NORM FORMS

    • Authors: JAMES MAYNARD
      Abstract: Let $K=\mathbb{Q}(\unicode[STIX]{x1D714})$ with $\unicode[STIX]{x1D714}$ the root of a degree $n$ monic irreducible polynomial $f\in \mathbb{Z}[X]$ . We show that the degree $n$ polynomial $N(\sum _{i=1}^{n-k}x_{i}\unicode[STIX]{x1D714}^{i-1})$ in $n-k$ variables takes the expected asymptotic number of prime values if $n\geqslant 4k$ . In the special case $K=\mathbb{Q}(\sqrt[n]{\unicode[STIX]{x1D703}})$ , we show that $N(\sum _{i=1}^{n-k}x_{i}\sqrt[n]{\unicode[STIX]{x1D703}^{i-1}})$ takes infinitely many prime values, provided $n\geqslant 22k/7$ .Our proof relies on using suitable ‘Type I’ and ‘Type II’ esti...
      PubDate: 2020-02-06T00:00:00.000Z
      DOI: 10.1017/fmp.2019.8
      Issue No: Vol. 8 (2020)
       
  • CHARACTER LEVELS AND CHARACTER BOUNDS

    • Authors: ROBERT M. GURALNICK; MICHAEL LARSEN, PHAM HUU TIEP
      Abstract: We develop the concept of character level for the complex irreducible characters of finite, general or special, linear and unitary groups. We give characterizations of the level of a character in terms of its Lusztig label and in terms of its degree. Then we prove explicit upper bounds for character values at elements with not-too-large centralizers and derive upper bounds on the covering number and mixing time of random walks corresponding to these conjugacy classes. We also characterize the level of the character in terms of certain dual pairs and prove explicit exponential character bounds for the character values, provided that the level is not too large. Several further applications are also provided. Related results for other finite classical groups are obtained in the sequel [Guralnick et al. ‘Character levels and character bounds for finite classical groups’, Preprint, 2019, arXiv:1904.08070] by different methods.
      PubDate: 2020-01-24T00:00:00.000Z
      DOI: 10.1017/fmp.2019.9
      Issue No: Vol. 8 (2020)
       
  • MOMENTS OF RANDOM MULTIPLICATIVE FUNCTIONS, I: LOW MOMENTS, BETTER THAN
           SQUAREROOT CANCELLATION, AND CRITICAL MULTIPLICATIVE CHAOS

    • Authors: ADAM J. HARPER
      Abstract: We determine the order of magnitude of $\mathbb{E}|\sum _{n\leqslant x}f(n)|^{2q}$ , where $f(n)$ is a Steinhaus or Rademacher random multiplicative function, and $0\leqslant q\leqslant 1$ . In the Steinhaus case, this is equivalent to determining the order of $\lim _{T\rightarrow \infty }\frac{1}{T}\int _{0}^{T}|\sum _{n\leqslant x}n^{-it}|^{2q}\,dt$ .In particular, we find that $\mathbb{E}|\sum _{n\leqslant x}f(n)|\asymp \sqrt{x}/(\log \log x)^{1/4}$ . This proves a conjecture of Helson that one should have better than squareroot cancellation in the first moment and disproves counter-conjectures of various other authors. We deduce some consequences for the distribution and large deviations of $\sum _{n\leqslant x}f(n)$ .The proofs develop a connection between $\mathbb{E}|\sum _{n\leqslant x}f(n)|^{2q}$ and the $q$ th moment of a critical, approximately Gaussian, multiplicative chaos and then establish the required estimates for that. We include some general introductory discussion about critical multiplicative chaos to help readers unfamiliar with that area.
      PubDate: 2020-01-20T00:00:00.000Z
      DOI: 10.1017/fmp.2019.7
      Issue No: Vol. 8 (2020)
       
 
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