Bounds for Modular L-functions in the Level Aspect
نویسنده
چکیده
Let f be a primitive (holomorphic or Maaß) cusp form of level q and nontrivial 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). Résumé. Soit f une forme modulaire cuspidale primitive (holomorphe ou de Maaß) de niveau q et de caractère central non-trivial. Alors, pour Re s = 1 2 , la function L associée vérifie L(f, s) q 1 4 − 1 1889 , où la constante implicite dépend polynômialement de s et du paramètre archimédien de f (le poids ou la valeur propre du Laplacien).
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