Non-vanishing of symmetric square -functions

Author:
Yuk-Kam Lau

Journal:
Proc. Amer. Math. Soc. **130** (2002), 3133-3139

MSC (2000):
Primary 11F66

Published electronically:
May 29, 2002

MathSciNet review:
1912989

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a complex number with , we study the existence of a cusp form of large even weight for the full modular group such that its associated symmetric square -function does not vanish. This problem is also considered in other articles.

**1.**Harold Davenport,*Multiplicative number theory*, 2nd ed., Graduate Texts in Mathematics, vol. 74, Springer-Verlag, New York-Berlin, 1980. Revised by Hugh L. Montgomery. MR**606931****2.**G. H. Hardy and E. M. Wright,*An introduction to the theory of numbers*, 5th ed., The Clarendon Press, Oxford University Press, New York, 1979. MR**568909****3.**Winfried Kohnen and Jyoti Sengupta,*Nonvanishing of symmetric square 𝐿-functions of cusp forms inside the critical strip*, Proc. Amer. Math. Soc.**128**(2000), no. 6, 1641–1646. MR**1676328**, 10.1090/S0002-9939-99-05419-2**4.**Xian-Jin Li,*On the poles of Rankin-Selberg convolutions of modular forms*, Trans. Amer. Math. Soc.**348**(1996), no. 3, 1213–1234. MR**1333393**, 10.1090/S0002-9947-96-01540-1**5.**Goro Shimura,*On the holomorphy of certain Dirichlet series*, Proc. London Math. Soc. (3)**31**(1975), no. 1, 79–98. MR**0382176****6.**G. N. Watson,*A treatise on the theory of Bessel functions*, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR**1349110**

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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:
http://dx.doi.org/10.1090/S0002-9939-02-06712-6

Received by editor(s):
February 6, 2001

Published electronically:
May 29, 2002

Communicated by:
Dennis A. Hejhal

Article copyright:
© Copyright 2002
American Mathematical Society