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arXiv · 1811.12521

An elementary bound on Siegel zeroes

Thomas Morrill·Tim Trudgian
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Abstract

We consider Dirichlet $L$-functions $L(s, χ)$ where $χ$ is a real, non-principal character modulo $q$. Using Pintz's refinement of Page's theorem, we prove that for $q\geq 3$ the function $L(s, χ)$ has at most one real zero $β$ with $1- 1.011/\log q < β< 1$.

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Thomas Morrill, Tim Trudgian. 2018-11-29. An elementary bound on Siegel zeroes. https://arxiv.org/abs/1811.12521

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