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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Non-vanishing of symmetric square $L$-functions

Author(s): Yuk-Kam Lau
Journal: Proc. Amer. Math. Soc. 130 (2002), 3133-3139.
MSC (2000): Primary 11F66
Posted: May 29, 2002
MathSciNet review: 1912989
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Abstract | References | Similar articles | Additional information

Abstract: Given a complex number $s$ with $0<\Re e\, s<1$, we study the existence of a cusp form of large even weight for the full modular group such that its associated symmetric square $L$-function $L({sym}^2f,s)$ does not vanish. This problem is also considered in other articles.


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G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers, Fifth edition, Oxford University Press, 1979. MR 81i:10002

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W. Kohnen and J. Sengupta, Nonvanishing of symmetric square $L$-functions of cusp forms inside the critical strip, Proc. Amer. Math. Soc. 128 (2000), 1641-1646. MR 2000j:11072

4.
X.-J. Li, On the poles of Rankin-Selberg convolution of modular forms, Trans. Amer. Math. Soc. 348 (1996), 1213-1234. MR 96h:11038

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G. Shimura, On the holomorphy of certain Dirichlet series, Proc. London Math. Soc. 31 (1975), 79-98. MR 52:3064

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G.N. Watson, A Treatise on the Theory of Bessel Function, Reprint, Cambridge University Press, 1996. MR 96i:33010

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Additional Information:

Yuk-Kam Lau
Affiliation: Institut Élie Cartan, Université Henri Poincaré (Nancy 1), 54506 Vandoeuvre lés Nancy Cedex, France
Address at time of publication: Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
Email: yklau@maths.hku.hk

DOI: 10.1090/S0002-9939-02-06712-6
PII: S 0002-9939(02)06712-6
Received by editor(s): February 6, 2001
Posted: May 29, 2002
Communicated by: Dennis A. Hejhal
Copyright of article: Copyright 2002, American Mathematical Society




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