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arXiv · 1602.07256

Effective Lower Bounds for L(1,{\chi}) via Eisenstein Series

Peter Humphries
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Abstract

We give effective lower bounds for $L(1,\chi)$ via Eisenstein series on $\Gamma_0(q) \backslash \mathbb{H}$. The proof uses the Maass-Selberg relation for truncated Eisenstein series and sieve theory in the form of the Brun-Titchmarsh inequality. The method follows closely the work of Sarnak in using Eisenstein series to find effective lower bounds for $\zeta(1+it)$.

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Peter Humphries. 2016-02-23. Effective Lower Bounds for L(1,{\chi}) via Eisenstein Series. https://doi.org/10.2140/pjm.2017.288.355

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