A Note on the Mean Value of L--functions in Function Fields

2012/08/13 by Julio Andrade, Andrade, Julio
Mathematics · #11G20 (Primary) 11R29 #14G10 (Secondary) #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G20 #msc:11R29 #msc:14G10

paper · pdf · doi:10.48550/arxiv.1208.2633

Accepted for publication in International Journal of Number Theory

arxiv created 2012/08/13 · arxiv updated 2012/08/14

Abstract

An asymptotic formula for the sum ∑ L(1,χ) is established for a family of hyperelliptic curves of genus g over a fixed finite field \mathbbF_q as g→∞ making use of the analogue of the approximate functional equation for such L--functions. As a corollary, we obtain a formula for the average of the class number of the associated rings \mathbbF_q[T,sqrtD].

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