REAL

Hybrid bounds for twisted L-functions

Blomer, Valentin and Harcos, Gergely (2008) Hybrid bounds for twisted L-functions. Journal für die reine und angewandte Mathematik, 2008 (621). pp. 53-79. ISSN 0075-4102

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Abstract

The aim of this paper is to derive bounds on the critical line Rs 1/2 for L- functions attached to twists f circle times chi of a primitive cusp form f of level N and a primitive character modulo q that break convexity simultaneously in the s and q aspects. If f has trivial nebentypus, it is shown that L(f circle times chi, s) << (N vertical bar s vertical bar q)(epsilon) N-4/5(vertical bar s vertical bar q)(1/2-1/40), where the implied constant depends only on epsilon > 0 and the archimedean parameter of f. To this end, two independent methods are employed to show L(f circle times chi, s) << (N vertical bar s vertical bar q)(epsilon) N-1/2 vertical bar S vertical bar(1/2)q(3/8) and L(g,s) << D-2/3 vertical bar S vertical bar(5/12) for any primitive cusp form g of level D and arbitrary nebentypus (not necessarily a twist f circle times chi of level D vertical bar Nq(2)).

Item Type: Article
Subjects: Q Science / természettudomány > QA Mathematics / matematika
Depositing User: Erika Bilicsi
Date Deposited: 25 Feb 2013 08:40
Last Modified: 25 Feb 2013 08:40
URI: http://real.mtak.hu/id/eprint/4276

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