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manuscripta mathematica

, Volume 104, Issue 1, pp 1–19 | Cite as

Deux théorèmes de non-annulation de valeurs spéciales de fonctions L

  • E. Kowalski
  • P. Michel

Abstract:

In answer to questions recently raised by Merel [Mer], we prove two non-vanishing theorems for the central value of automorphic L-functions: let p be prime and let χ be a primitive character modulo p. Then for all p large enough

1. If χ is not quadratic and even, there exists a primitive weight 2 form f of level p with \(\).

2. If χ is quadratic and even, then there exists a primitive weight 2 form f of level p with \(\).

Mathematics Subject Classification (2000): 11F67, 11M99 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • E. Kowalski
    • 1
  • P. Michel
    • 2
  1. 1.Department of Mathematics, Fine Hall, Princeton University, Princeton, NJ 08544-1000, USA. E-mail: ekowalsk@math.princeton.eduUS
  2. 2.Université Montpellier II, CC 051, 34095 Montpellier Cedex 05, France.¶e-mail: michel@darboux.math.univ-montp2.frFR

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