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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 ⊗ χ 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
,
where the implied constant depends only on ε > 0 and the archimedean parameter of f. To this end, two independent methods are employed to show
and
for any primitive cusp form g of level D and arbitrary nebentypus (not necessarily a twist f ⊗ χ of level D | Nq2).
Received: 2006-07-06
Published Online: 2008-07-01
Published in Print: 2008-August
© Walter de Gruyter Berlin · New York 2008
