Non-vanishing of symmetric square -functions

Author:
Yuk-Kam Lau

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

MSC (2000):
Primary 11F66

DOI:
https://doi.org/10.1090/S0002-9939-02-06712-6

Published electronically:
May 29, 2002

MathSciNet review:
1912989

Full-text PDF

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.**H. Davenport,*Multiplicative Number Theory*, Second edition, Springer-Verlag, 1980. MR**82m:10001****2.**G.H. Hardy and E.M. Wright,*An Introduction to the Theory of Numbers*, Fifth edition, Oxford University Press, 1979. MR**81i:10002****3.**W. Kohnen and J. Sengupta,*Nonvanishing of symmetric square**-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****5.**G. Shimura,*On the holomorphy of certain Dirichlet series*, Proc. London Math. Soc.**31**(1975), 79-98. MR**52:3064****6.**G.N. Watson,*A Treatise on the Theory of Bessel Function*, Reprint, Cambridge University Press, 1996. MR**96i:33010**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
11F66

Retrieve articles in all journals with MSC (2000): 11F66

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:
https://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