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124 papers · 1 filter
Transcendence of multivariate Mahler functions and algebraic relations between their values
Enzo Brechler
We study the functional properties of Mahler functions of several variables associated with a large class of Mahler transformations. We prove that these functions are always analyt…
Remarks on a theorem of Silverman
Khai-Hoan Nguyen-Dang, Quang-Khai Nguyen
Motivated by a theorem of Silverman, we consider the following problem. Let be an abelian variety over a global field . Given a non-torsion point , for a suffici…
Bailey pairs and quantum -series identites. I. The classical identities
Jehanne Dousse, Jeremy Lovejoy
We use Bailey pairs to prove -series identities at roots of unity due to Cohen and Bryson-Ono-Pitman-Rhoades. The proofs use Bailey pairs with quadratic forms developed in the s…
On the constituents of the mod cohomology of Shimura curves
Christophe Breuil, Florian Herzig, Yongquan Hu +2
Let be a prime number and a finite unramified extension of . When is large enough with respect to and under mild genericity assumptions…
Galois groups of reductions modulo p of D-finite series
Xavier Caruso, Florian Fürnsinn, Daniel Vargas-Montoya
The aim of this paper is to investigate the algebraicity behavior of reductions of -finite power series modulo prime numbers. For many classes of D-finite functions, such as dia…
Bounds for moments of quadratic character sums and theta functions
Marc Munsch, Yuichiro Toma
In this paper, we investigate the size of moments of quadratic character sums averaged over the family of fundamental discriminants. We obtain an asymptotic formula for all integer…