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70 papers · 1 filter
The trigonometric polynomial on sums of two squares, an additive problem and generalisation
Olivier Ramare, GK Viswanadham
Let be the set of odd integers that are sums of two coprime squares. We prove that the trigonometric polynomial satisfies \[ \frac{S(α; N)}…
Introduction to the relative Langlands program
Raphaël Beuzart-Plessis
The aim of these notes is to give an overview of several aspects of what has come to be called the relative Langlands program, a theme that takes its origin in the study of automor…
On twisted period functions and Moments of a weighted mean square of Dirichlet L-functions on the critical line
Sebastien Darses, Berend Ringeling, Emmanuel Royer
We extend to Dirichlet L-functions associated with arbitrary primitive characters a range of objects and properties -- including Eisenstein series and period functions -- that were…
On the Weil descent of Artin-Schreier algebraic function fields over finite fields
Stéphane Ballet, Robert Rolland
Let us consider a generalized Artin-Schreier algebraic function field extension of the rational function field $\F_{p^n}(x)$ defined over the finite field extension $K=\F_{p^n}…
Étude statistique du facteur premier médian, 3 : lois de répartition
Jonathan Rotgé
We consider the Gaussian limit law for the distribution of the middle prime factor of an integer, defined according to multiplicity or not. We obtain an optimal bound for the speed…
Chaining Multiplications in Finite Fields with Chudnovsky-type Algorithms and Tensor Rank of the k-multiplication
Stéphane Ballet, Robert Rolland
We design a class of Chudnovsky-type algorithms multiplying k elements of a finite extension of order n a finite field K. We prove that these algorithms give a tensor decomposition…