Vol. 288, No. 2, 2017

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ISSN: 0030-8730
Effective lower bounds for $L(1,\chi)$ via Eisenstein series

Peter Humphries

Vol. 288 (2017), No. 2, 355–375
Abstract

We give effective lower bounds for L(1,χ) via Eisenstein series on Γ0(q) . 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 ζ(1 + it).

Keywords
Dirichlet $L$-function, lower bounds, Eisenstein series
Mathematical Subject Classification 2010
Primary: 11M20
Secondary: 11M36
Milestones
Received: 14 June 2016
Accepted: 23 December 2016
Published: 28 April 2017
Authors
Peter Humphries
Department of Mathematics
Princeton University
Princeton, NJ 08544
United States