Moments of Dirichlet L-functions with prime conductors over function\n fields

2019/09/02 by Hung M. Bui, Alexandra Florea, Bui, Hung M. +1
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1909.00854

openalex publication_date 2019/09/02 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We compute the second moment in the family of quadratic Dirichlet\nL-functions with prime conductors over mathbbF_q[x] when the degree of\nthe discriminant goes to infinity, obtaining one of the lower order terms. We\nalso obtain an asymptotic formula with the leading order term for the mean\nvalue of the derivatives of L-functions associated to quadratic twists of a\nfixed elliptic curve over mathbbF_q(t) by monic irreducible polynomials,\nwhich allows us to show that there exists a monic irreducible polynomial such\nthat the analytic rank of the corresponding twisted elliptic curve is equal to\n1.\n

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