A Note on Twisted Moments of Dirichlet L-functions

2023/06/14 by Andrade, J. C., MacMillan, J.
#11M06 #11M38 #11T06 #11T55 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2306.08493

Abstract

In this paper, we establish an asymptotic formula for the twisted second moments of Dirichlet L-functions with one and two twists when averaged over all primitive Dirichlet characters of modulus R, where R is a monic polynomial in \mathbbF_q[T]. The main result in this paper generalizes the work of Djanković [`The reciprocity law for the twisted second moment of Dirichlet L-functions over rational function fields', Bull. Aust. Math. Soc. 98 (2018), no. 3, 382--388].

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