Large values of $L(\sigma,\chi)$ for subgroups of characters
Number Theory
2026-04-06 v1
Abstract
We obtain (conditional and unconditional) results on large values of -functions in the critical strip when the character runs through a thin subgroup of all characters modulo an integer . Some of these bounds are based on new zero-density estimates on average over a subgroup of characters. These bounds follow from a mean value estimate for character sums, which is based on the work of D. R. Heath-Brown (1979). As yet another application of this mean value estimate, we obtain an unconditional version of a conditional (on the Generalised Riemann Hypothesis) result of Z. Rudnick and A. Zaharescu (2000) about gaps between primitive roots.
Keywords
Cite
@article{arxiv.2604.02960,
title = {Large values of $L(\sigma,\chi)$ for subgroups of characters},
author = {Pranendu Darbar and Bryce Kerr and Marc Munsch and Igor Shparlinski},
journal= {arXiv preprint arXiv:2604.02960},
year = {2026}
}