Wide moments of $L$-functions II: Dirichlet $L$-functions

Asbjørn Christian Nordentoft

Wide moments of $L$-functions II: Dirichlet $L$-functions

Number Theory 2024-10-30 v2

Authors: Asbjørn Christian Nordentoft

Abstract

We study wide moments of Dirichlet $L$ -functions using analytic properties of the Lerch zeta function. Among other things we obtain an asymptotic expansion of wide moments of Dirichlet $L$ -functions (with arbitrary twists) extending results of Heath-Brown. We also give applications to non-vanishing.

Keywords

wide moments dirichlet l-functions lerch zeta function asymptotic expansion non-vanishing

Cite

@article{arxiv.2111.03834,
  title  = {Wide moments of $L$-functions II: Dirichlet $L$-functions},
  author = {Asbjørn Christian Nordentoft},
  journal= {arXiv preprint arXiv:2111.03834},
  year   = {2024}
}

Comments

Proposition 2.4 in the previous version was wrong (note that this does not affect any of the results stated in the introduction). We have corrected the statement and proof, 20 pages

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