The First Moment of Dirichlet L-functions over Generators of the Character Group

Rizwanur Khan

The First Moment of Dirichlet L-functions over Generators of the Character Group

Number Theory 2026-07-16 v1

Authors: Rizwanur Khan

Abstract

We evaluate the average of the central values $L(1/2,\chi)$ over the generators of the group of Dirichlet characters modulo $q$ , as $q\to\infty$ through the primes.

Keywords

Dirichlet L-function first moment character group central value prime modulus

Cite

@article{arxiv.2607.14612,
  title  = {The First Moment of Dirichlet L-functions over Generators of the Character Group},
  author = {Rizwanur Khan},
  journal= {arXiv preprint arXiv:2607.14612},
  year   = {2026}
}