Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Non-vanishing of symmetric square $L$-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
Full-text PDF Free Access

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.


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

  • 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 $L$-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
  • 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

Similar Articles

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: http://dx.doi.org/10.1090/S0002-9939-02-06712-6
PII: S 0002-9939(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