Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-13T07:01:40.619Z Has data issue: false hasContentIssue false
  • English
  • Français

On the average of central values of symmetric square L-functions in weight aspect

Published online by Cambridge University Press:  22 January 2016

Winfried Kohnen  and
Jyoti Sengupta
Winfried Kohnen
Affiliation:
Universität Heidelberg Mathematisches Institut, INF 288 D-69120 Heidelberg, Germany, winfried@mathi.uni-heidelberg.de
Jyoti Sengupta
Affiliation:
T.I.F.R. School of Mathematics, Homi Bhabha Road 400 005 Bombay, India, sengupta@math.tifr.res.in
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is proved that the central values of symmetric square L-functions of normalized Hecke eigenforms for the full modular group on average satisfy an analogue of the Lindelöf hypothesis in weight aspect, under the assumption that these values are non-negative.

Keywords

11F03
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 167 , 2002 , pp. 95 - 100
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

References

[1] Abramowitz, M. and Stegun, I., Handbook of mathematical functions, Dover, New York, 1965.Google Scholar
[2] Apostol, T., Introduction to Analytic Number Theory, Springer, Berlin-Heidelberg-New York, 1976.Google Scholar
[3] Gelbart, S. and Jacquet, H., A relation between automorphic representations of GL2 and GL3 , Ann. Sci. École Normale Sup. 4e série, 11 (1978), 471–552.Google Scholar
[4] Iwaniec, H., Small eigenvalues of Laplacian for Γ0(N), Acta Arith., 16 (1990), 65–82.CrossRefGoogle Scholar
[5] Kohnen, W. and Sengupta, J., Nonvanishing of symmetric square L-functions of cusp forms inside the critical strip, Proc. Amer. Math. Soc., 128, no. 6 (2000), 1641–1646.Google Scholar
[6] Kohnen, W. and Sengupta, J., On quadratic character twists of Hecke L-functions attached to cusp forms of varying weights at the central point, Acta Arith., XCIX.1 (2001), 61–66.Google Scholar
[7] Sarnak, P., L-functions. Documenta Mathematica, extra vol. ICM 1998, I pp. 453–465.Google Scholar
[8] Sengupta, J., The central critical value of automorphic L-functions, C.R. Math. Rep. Acad. Sci. Canada, 22 (2) (2000), 82–85.Google Scholar
[9] Shimura, G., On the holomorphy of certain Dirichlet series, Proc. London Math. Soc., 31 (1975), 75–98.Google Scholar
[10] Zagier, D., Modular forms whose Fourier coefficients involve zeta-functions of quadratic fields, In: Modular Functions of One variable VI (eds. Serre, J.-P. and Zagier, D.), pp. 105–169, LNM no. 627, Springer, Berlin-Heidelberg-New York, 1976.Google Scholar