Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:Li; Junxian Pages: 1459 - 1505 Abstract: In this paper, we are interested in obtaining large values of Dirichlet L-functions evaluated at zeros of a class of L-functions, that is, where is a primitive Dirichlet character and F belongs to a class of L-functions. The class we consider includes L-functions associated with automorphic representations of over . PubDate: 2020-07-01 DOI: 10.4153/S0008414X20000577

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Authors:Greither; Cornelius, Kučera, Radan Pages: 1506 - 1530 Abstract: The aim of this paper is to study circular units in the compositum K of t cyclic extensions of () of the same odd prime degree . If these fields are pairwise arithmetically orthogonal and the number s of primes ramifying in is larger than then a nontrivial root of the top generator of the group of circular units of K is constructed. This explicit unit is used to define an enlarged group of circular units of K, to show that divides the class number of K, and to prove an annihilation statement for the ideal class group of K. PubDate: 2020-07-14 DOI: 10.4153/S0008414X20000589

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Authors:Angel; Omer, Holroyd, Alexander E., Hutchcroft, Tom, Levy, Avi Pages: 1531 - 1555 Abstract: We show that the Mallows measure on permutations of arises as the law of the unique Gale–Shapley stable matching of the random bipartite graph with vertex set conditioned to be perfect, where preferences arise from the natural total ordering of the vertices of each gender but are restricted to the (random) edges of the graph. We extend this correspondence to infinite intervals, for which the situation is more intricate. We prove that almost surely, every stable matching of the random bipartite graph obtained by performing Bernoulli percolation on the complete bipartite graph falls into one of two classes: a countable family of tame stable matchings, in which the length of the longest edge crossing k is as , and an uncountable family of wild stable matchings, in which this length is as . The tame stable matching has the law of the Mallows permutation of (as constructed by Gnedin and Olshanski) composed with the shift . The permutation dominates PubDate: 2020-07-27 DOI: 10.4153/S0008414X20000590

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Authors:Heittokangas; Janne, Yu, Hui, Zemirni, Mohamed Amine Pages: 1556 - 1591 Abstract: A classical theorem of Frei states that if is the last transcendental function in the sequence of entire functions, then each solution base of the differential equation contains at least entire functions of infinite order. Here, the transcendental coefficient dominates the growth of the polynomial coefficients . By expressing the dominance of in different ways and allowing the coefficients to be transcendental, we show that the conclusion of Frei’s theorem still holds along with an additional estimation on the asymptotic lower bound for the growth of solutions. At times, these new refined results give a larger number of linearly independent solutions of infinite order than the original theorem of Frei. For such solutions, we show that is the only possible finite deficient value. Previously, this property has been known to hold for so-called admissible solutions and is commonly cited as Wittich’s theorem. Analogous results are discussed for linear differential equations in the unit disc, as well as for complex difference and complex q-difference equations. PubDate: 2020-07-30 DOI: 10.4153/S0008414X20000607

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Authors:Gonçalves; Daniel, Steinberg, Benjamin Pages: 1592 - 1626 Abstract: Given an action of inverse semigroup S on a ring A (with domain of denoted by ), we show that if the ideals , with e an idempotent, are unital, then the skew inverse semigroup ring can be realized as the convolution algebra of an ample groupoid with coefficients in a sheaf of (unital) rings. Conversely, we show that the convolution algebra of an ample groupoid with coefficients in a sheaf of rings is isomorphic to a skew inverse semigroup ring of this sort. We recover known results in the literature for Steinberg algebras over a field as special cases. PubDate: 2020-08-07 DOI: 10.4153/S0008414X20000619

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Authors:Kabluchko; Zakhar, Temesvari, Daniel, Thäle, Christoph Pages: 1627 - 1647 Abstract: A new approach to prove weak convergence of random polytopes on the space of compact convex sets is presented. This is used to show that the profile of the rescaled Schläfli random cone of a random conical tessellation, generated by n independent and uniformly distributed random linear hyperplanes in , weakly converges to the typical cell of a stationary and isotropic Poisson hyperplane tessellation in , as . PubDate: 2020-08-11 DOI: 10.4153/S0008414X20000620

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Authors:Füredi; Zoltán, Jiang, Tao, Kostochka, Alexandr, Mubayi, Dhruv, Verstraëte, Jacques Pages: 1648 - 1666 Abstract: An ordered hypergraph is a hypergraph whose vertex set is linearly ordered, and a convex geometric hypergraph is a hypergraph whose vertex set is cyclically ordered. Extremal problems for ordered and convex geometric graphs have a rich history with applications to a variety of problems in combinatorial geometry. In this paper, we consider analogous extremal problems for uniform hypergraphs, and determine the order of magnitude of the extremal function for various ordered and convex geometric paths and matchings. Our results generalize earlier works of Braß–Károlyi–Valtr, Capoyleas–Pach, and Aronov–Dujmovič–Morin–Ooms-da Silveira. We also provide a new variation of the Erdős-Ko-Rado theorem in the ordered setting. PubDate: 2020-08-10 DOI: 10.4153/S0008414X20000632

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Authors:Guo; Weichao, Wu, Huoxiong, Yang, Dongyong Pages: 1667 - 1697 Abstract: A new characterization of is established replying upon local mean oscillations. Some characterizations of iterated compact commutators on weighted Lebesgue spaces are given, which are new even in the unweighted setting for the first order commutators. PubDate: 2020-08-20 DOI: 10.4153/S0008414X20000644

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Authors:Neumann; Daniel López Pages: 1698 - 1742 Abstract: We construct quantum invariants of balanced sutured 3-manifolds with a structure out of an involutive (possibly nonunimodular) Hopf superalgebra H. If H is the Borel subalgebra of , we show that our invariant is computed via Fox calculus, and it is a normalization of Reidemeister torsion. The invariant is defined via a modification of a construction of Kuperberg, where we use the structure to take care of the nonunimodularity of H or . PubDate: 2020-08-20 DOI: 10.4153/S0008414X20000656

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Authors:Massuyeau; Gwénaël, Moussard, Delphine Pages: 1743 - 1770 Abstract: We prove a “splicing formula” for the LMO invariant, which is the universal finite-type invariant of rational homology three-spheres. Specifically, if a rational homology three-sphere M is obtained by gluing the exteriors of two framed knots and in rational homology three-spheres, our formula expresses the LMO invariant of M in terms of the Kontsevich–LMO invariants of and . The proof uses the techniques that Bar-Natan and Lawrence developed to obtain a rational surgery formula for the LMO invariant. In low degrees, we recover Fujita’s formula for the Casson–Walker invariant, and we observe that the second term of the Ohtsuki series is not additive under “standard” splicing. The splicing formula also works when each comes with a link in addition to the knot , hence we get a “satellite formula” for the Kontsevich–LMO invariant. PubDate: 2020-08-20 DOI: 10.4153/S0008414X20000668