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

Debmalya Basak; Kyle Pratt

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arXiv · 2607.06433

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

Debmalya Basak·Kyle Pratt

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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 $s=1$.

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Debmalya Basak, Kyle Pratt. 2026-07-07. A Conditional Refinement of Page's Theorem on zeros of Dirichlet $L$-functions. https://arxiv.org/abs/2607.06433

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