23-27 June 2014
Université Lille 1
Europe/Paris timezone

Some Problems in Analytic Number Theory for Polynomials over Finite Fields

23 Jun 2014, 15:45
Salle de réunions (Université Lille 1)

Salle de réunions

Université Lille 1

U.M.R. CNRS 8524 U.F.R. de Mathématiques 59 655 Villeneuve d'Ascq Cédex
Analytic-Additive Number Theory Analytic-Additive Number Theory


Julio Andrade (IHES)


In this talk I will explore some traditional problems of analytic number theory in the context of function fields over a finite field. Several such problems which are currently viewed as intractable can, in the function field scenario, be attacked with vastly different tools than those of traditional analytic number theory. The resulting theorems in the function field setting can be used to check existing conjectures in the classical case, and to generate new ones. The problems I will discuss include: the twin prime conjecture, the additive divisor problem, moments of L-functions and connections with random matrix theory.

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