Authors:Bari; Naveed S., Hunsicker, Eugenie Pages: 281 - 325 Abstract: We answer Mark Kac’s famous question, “Can one hear the shape of a drum'” in the positive for orbifolds that are 3-dimensional and 4-dimensional lens spaces; we thus complete the answer to this question for orbifold lens spaces in all dimensions. We also show that the coefficients of the asymptotic expansion of the trace of the heat kernel are not sufficient to determine the above results. PubDate: 2019-08-27 DOI: 10.4153/S0008414X19000178

Authors:Baruch; Ehud Moshe, Purkait, Soma Pages: 326 - 372 Abstract: We study genuine local Hecke algebras of the Iwahori type of the double cover of and translate the generators and relations to classical operators on the space , odd and square-free. In [9] Manickam, Ramakrishnan, and Vasudevan defined the new space of that maps Hecke isomorphically onto the space of newforms of . We characterize this newspace as a common -eigenspace of a certain pair of conjugate operators that come from local Hecke algebras. We use the classical Hecke operators and relations that we obtain to give a new proof of the results in [9] and to prove our characterization result. PubDate: 2019-10-31 DOI: 10.4153/S0008414X19000233

Authors:Bindini; Ugo Pages: 373 - 391 Abstract: We consider a multimarginal transport problem with repulsive cost, where the marginals are all equal to a fixed probability . We prove that, if the concentration of is less than , then the problem has a solution of finite cost. The result is sharp, in the sense that there exists with concentration for which the cost is infinite. PubDate: 2019-05-07 DOI: 10.4153/S0008414X18000664

Authors:Byszewski; Jakub, Konieczny, Jakub Pages: 392 - 426 Abstract: We conjecture that bounded generalised polynomial functions cannot be generated by finite automata, except for the trivial case when they are ultimately periodic.Using methods from ergodic theory, we are able to partially resolve this conjecture, proving that any hypothetical counterexample is periodic away from a very sparse and structured set. In particular, we show that for a polynomial with at least one irrational coefficient (except for the constant one) and integer , the sequence is never automatic.We also prove that the conjecture is equivalent to the claim that the set of powers of an integer is not given by a generalised polynomial. PubDate: 2019-06-13 DOI: 10.4153/S0008414X19000038

Authors:Gao; Peng, Zhao, Liangyi Pages: 427 - 454 Abstract: In this paper we prove some one-level density results for the low-lying zeros of families of quadratic and quartic Hecke -functions of the Gaussian field. As corollaries, we deduce that at least 94.27% and 5%, respectively, of the members of the quadratic family and the quartic family do not vanish at the central point. PubDate: 2019-08-30 DOI: 10.4153/S0008414X1900021X

Authors:Hou; Shaoxiong, Ye, Deping Pages: 455 - 479 Abstract: This paper provides a functional analogue of the recently initiated dual Orlicz–Brunn–Minkowski theory for star bodies. We first propose the Orlicz addition of measures, and establish the dual functional Orlicz–Brunn–Minkowski inequality. Based on a family of linear Orlicz additions of two measures, we provide an interpretation for the famous -divergence. Jensen’s inequality for integrals is also proved to be equivalent to the newly established dual functional Orlicz–Brunn–Minkowski inequality. An optimization problem for the -divergence is proposed, and related functional affine isoperimetric inequalities are established. PubDate: 2019-07-16 DOI: 10.4153/S0008414X19000117

Authors:Kılıçer; Pınar, Lorenzo García, Elisa, Streng, Marco Pages: 480 - 504 Abstract: We give a bound on the primes dividing the denominators of invariants of Picard curves of genus 3 with complex multiplication. Unlike earlier bounds in genus 2 and 3, our bound is based, not on bad reduction of curves, but on a very explicit type of good reduction. This approach simultaneously yields a simplification of the proof and much sharper bounds. In fact, unlike all previous bounds for genus 3, our bound is sharp enough for use in explicit constructions of Picard curves. PubDate: 2019-05-07 DOI: 10.4153/S0008414X18000111

Authors:Laterveer; Robert, Vial, Charles Pages: 505 - 536 Abstract: This note is about certain locally complete families of Calabi–Yau varieties constructed by Cynk and Hulek, and certain varieties constructed by Schreieder. We prove that the cycle class map on the Chow ring of powers of these varieties admits a section, and that these varieties admit a multiplicative self-dual Chow–Künneth decomposition. As a consequence of both results, we prove that the subring of the Chow ring generated by divisors, Chern classes, and intersections of two cycles of positive codimension injects into cohomology via the cycle class map. We also prove that the small diagonal of Schreieder surfaces admits a decomposition similar to that of K3 surfaces. As a by-product of our main result, we verify a conjecture of Voisin concerning zero-cycles on the self-product of Cynk–Hulek Calabi–Yau varieties, and in the odd-dimensional case we verify a conjecture of Voevodsky concerning smash-equivalence. Finally, in positive characteristic, we show that the supersingular Cynk–Hulek Calabi–Yau varieties provide examples of Calabi–Yau varieties with “degenerate” motive. PubDate: 2019-09-03 DOI: 10.4153/S0008414X19000191

Authors:Nevo; Eran, Pineda-Villavicencio, Guillermo, Ugon, Julien, Yost, David Pages: 537 - 556 Abstract: We study -vertex -dimensional polytopes with at most one nonsimplex facet with, say, vertices, called almost simplicial polytopes. We provide tight lower and upper bound theorems for these polytopes as functions of , and , thus generalizing the classical Lower Bound Theorem by Barnette and the Upper Bound Theorem by McMullen, which treat the case where . We characterize the minimizers and provide examples of maximizers for any . Our construction of maximizers is a generalization of cyclic polytopes, based on a suitable variation of the moment curve, and is of independent interest. PubDate: 2019-05-21 DOI: 10.4153/S0008414X18000123

Authors:Cameron; Jan, Smith, Roger R. Pages: 557 - 562 Abstract: This note corrects an error in our paper “A Galois correspondence for reduced crossed products of unital simple -algebras by discrete groups”, http://dx.doi.org/10.4153/CJM-2018-014-6. The main results of the original paper are unchanged. PubDate: 2019-05-30 DOI: 10.4153/S0008414X1900018X