The Ratios Conjecture and negative moments of L-functions

Abstract: The Ratios Conjecture is a wide-reaching, very general conjecture, predicting asymptotic formulas for averages of ratios of L–functions in families. The Ratios Conjecture has applications to many questions of interest in number theory, such as obtaining non-vanishing results for L-functions or computing the n-level correlations of zeros of L-functions. In this talk, I will describe some recent results on the Ratios Conjecture for the family of quadratic L-functions over function fields. I will also discuss the closely related problem of obtaining upper bounds for negative moments of L-functions, which allows us to prove partial results towards the Ratios Conjecture in the case of one over one, two over two and three over three L-functions. Part of the work is joint with H. Bui and J. Keating.

other condensed matterstatistical mechanicsstrongly correlated electronsgeneral relativity and quantum cosmologyHEP - theorymathematical physicsalgebraic geometrydifferential geometrydynamical systemsgroup theorynumber theoryquantum algebrarepresentation theory

Audience: researchers in the discipline

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Number theory, Arithmetic and Algebraic Geometry, and Physics

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