English

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

Number Theory 2017-09-20 v2

Abstract

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

Keywords

Cite

@article{arxiv.1602.07256,
  title  = {Effective Lower Bounds for L(1,{\chi}) via Eisenstein Series},
  author = {Peter Humphries},
  journal= {arXiv preprint arXiv:1602.07256},
  year   = {2017}
}

Comments

17 pages. To appear in Pacific Journal of Mathematics