Effective Lower Bounds for L(1,χ) via Eisenstein Series

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 $\zeta (1+it)$.

17 pages. To appear in Pacific Journal of Mathematics

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