Humphries, P;
(2017)
Effective lower bounds for L(1,χ) via Eisenstein series.
Pacific Journal of Mathematics
, 288
(2)
pp. 355-375.
10.2140/pjm.2017.288.355.
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Abstract
We give effective lower bounds for L(1,χ) via Eisenstein series on Γ0(q)∖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).
| Type: | Article |
|---|---|
| Title: | Effective lower bounds for L(1,χ) via Eisenstein series |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.2140/pjm.2017.288.355 |
| Publisher version: | http://dx.doi.org/10.2140/pjm.2017.288.355 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Dirichlet L-function, lower bounds, Eisenstein series |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1569445 |
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