Bounds for modular L-functions in the level aspect

Blomer, Valentin and Harcos, Gergely and Michel, Philippe (2007) Bounds for modular L-functions in the level aspect. Annales Scientifiques de l’École Normale Supérieure, 40 (5). pp. 697-740. ISSN 0012-9593

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Abstract

Let f be a primitive (holomorphic or Maa beta) cusp form of level q and non-trivial nebentypus. Then for Re s = 1/2 the associated L-function satisfies L(f, s) < << q(1/4 - 1/1889), where the implied constant depends polynomially on s and the Archimedean parameters of f (weight or Laplacian eigenvalue).

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