Some special values of hypergeometric series related to central values of automorphic L-functions

2013/05/25 by Akihito Ebisu, Ebisu, Akihito
Mathematics · #33C05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:33C05

paper · pdf · doi:10.48550/arxiv.1305.5891

11pages

arxiv created 2013/05/25 · arxiv updated 2013/05/28

Abstract

In a recent work, H.Narita presented problems concerning the strict positivity of central values of certain automorphic L-functions in the form of questions regarding special values of the hypergeometric series. In this paper, we present partial answers to these questions using the theory of orthogonal polynomials and three term relations of the hypergeometric series.

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