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Nonvanishing of symmetric square -functions of cusp forms inside the critical strip
Author(s):
Winfried
Kohnen;
Jyoti
Sengupta
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1641-1646.
MSC (2000):
Primary 11Fxx
Posted:
September 30, 1999
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Abstract:
We shall give a certain nonvanishing result for the symmetric square -function of an elliptic cuspidal Hecke eigenform w.r.t. the full modular group inside the critical strip.
References:
- [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]
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and , 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
, Invent. Math. 38, 1-16 (1976/77) MR 55:5583 - [5]
- W. Kohnen: Nonvanishing of Hecke
-functions associated to cusp forms inside the critical strip, J. of Number Theory vol. 67, no. 2, 182-189 (1997) MR 98j:11037 - [6]
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- 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
Email:
winfried@mathi.uni-heidelberg.de
Jyoti
Sengupta
Affiliation:
School of Mathematics, Tata Institute for Fundamental Research, Homi Bhabha Road, Bombay 400 005, India
Email:
sengupta@math.tifr.res.in
DOI:
10.1090/S0002-9939-99-05419-2
PII:
S 0002-9939(99)05419-2
Received by editor(s):
July 31, 1998
Posted:
September 30, 1999
Communicated by:
Dennis A. Hejhal
Copyright of article:
Copyright
2000,
American Mathematical Society
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