A Conditional Refinement of Page's Theorem on zeros of Dirichlet $L$-functions

Debmalya Basak; Kyle Pratt

A Conditional Refinement of Page's Theorem on zeros of Dirichlet $L$-functions

Number Theory 2026-07-07 v1

Authors: Debmalya Basak , Kyle Pratt

Abstract

Landau--Siegel zeros are hypothetical zeros of Dirichlet $L$ -functions that are close to the point $s=1$ . A classic theorem of Page shows at most one such zero can exist among all Dirichlet $L$ -functions with conductor $\leq Q$ . We show that one can significantly refine Page's theorem under the assumption that all non-real zeros of Dirichlet $L$ -functions lie outside a shrinking neighborhood of $s=1$ .

Keywords

landau-siegel zeros dirichlet l-functions page's theorem zeros refinement

Cite

@article{arxiv.2607.06433,
  title  = {A Conditional Refinement of Page's Theorem on zeros of Dirichlet $L$-functions},
  author = {Debmalya Basak and Kyle Pratt},
  journal= {arXiv preprint arXiv:2607.06433},
  year   = {2026}
}

Comments

9 pages, published in Research in Number Theory