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Proceedings of the American Mathematical Society

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Nonvanishing of symmetric square $L$-functions
of cusp forms inside the critical strip

Authors: Winfried Kohnen and Jyoti Sengupta
Journal: Proc. Amer. Math. Soc. 128 (2000), 1641-1646
MSC (2000): Primary 11Fxx
Published electronically: September 30, 1999
MathSciNet review: 1676328
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Abstract | References | Similar Articles | Additional Information

Abstract: We shall give a certain nonvanishing result for the symmetric square $L$-function of an elliptic cuspidal Hecke eigenform w.r.t. the full modular group inside the critical strip.

References [Enhancements On Off] (What's this?)

  • [1] N. Abramowitz and I. Stegun: ``Handbook of Mathematical Functions'', Dover, New York, 1965
  • [2] T. Apostol: ``Introduction to Analytic Number Theory'', Springer, Berin-Heidelberg-New York, 1976 MR 55:7892
  • [3] S. Gelbart and H. Jacquet: A relation between automorphic representations of $GL_{2}$ and $GL_{3}$, Ann. Sci. E.N.S. IV ser., 11, 471-542 (1978) MR 81e:10025
  • [4] H. Jacquet and J. A. Shalika: A nonvanishing theorem for zeta functions of $GL_{n}$, Invent. Math. 38, 1-16 (1976/77) MR 55:5583
  • [5] W. Kohnen: Nonvanishing of Hecke $L$-functions associated to cusp forms inside the critical strip, J. of Number Theory vol. 67, no. 2, 182-189 (1997) MR 98j:11037
  • [6] X.-J. Li: On the poles of Rankin-Selberg convolutions of modular forms, Trans. Amer. Math. Soc. 348, no. 3, 1213-1234 (1996) MR 96h:11038
  • [7] G. Shimura: On the holomorphy of certain Dirichlet series, Proc. London Math. Soc. 31, 75-98 (1975) MR 52:3064
  • [8] D. Zagier: Modular forms whose Fourier coefficients involve zeta-functions of quadratic fields, in ``Modular Functions of One Variable VI'' (eds. J.-P. Serre and D. Zagier), pp. 105-169, LNM no. 627, Springer, Berlin-Heidelberg-New York, 1976. MR 58:5525

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Additional Information

Winfried Kohnen
Affiliation: Universität Heidelberg, Mathematisches Institut, Im Neuenheimer, Feld 288, D-69120 Heidelberg, Germany

Jyoti Sengupta
Affiliation: School of Mathematics, Tata Institute for Fundamental Research, Homi Bhabha Road, Bombay 400 005, India

Received by editor(s): July 31, 1998
Published electronically: September 30, 1999
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 2000 American Mathematical Society

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