Granville, A;
Soundararajan, K;
(2018)
Large character sums: Burgess's theorem and zeros of L-functions.
Journal of the European Mathematical Society
, 20
(1)
pp. 1-14.
10.4171/JEMS/757.
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Abstract
We study the conjecture that ∑n≤xχ(n)=o(x) for any primitive Dirichlet character χ modulo q with x≥qϵ, which is known to be true if the Riemann Hypothesis holds for L(s,χ). We show that it holds under the weaker assumption that „100%" of the zeros of L(s,χ) up to height 1/4 lie on the critical line. We also establish various other consequences of having large character sums; for example, that if the conjecture holds for χ2 then it also holds for χ.
| Type: | Article |
|---|---|
| Title: | Large character sums: Burgess's theorem and zeros of L-functions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4171/JEMS/757 |
| Publisher version: | http://dx.doi.org/10.4171/JEMS/757 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Bounds on character sums, zeros of Dirichlet LL-functions, multiplicative functions |
| UCL classification: | UCL 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/1557191 |
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