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Rankin-Selberg method for Siegel cusp forms

Published online by Cambridge University Press:  22 January 2016

Tadashi Yamazaki
Tadashi Yamazaki*
Affiliation:
Department of Mathematics, Faculty of Science, Kyushu University, 33, Fukuoka 812, Japan
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Let Gn (resp. Γn) be the real symplectic (resp. Siegel modular) group of degree n. The Siegel cusp form is a holomorphic function on the Siegel upper half plane which satisfies functional equations relative to Γn and vanishes at the cusps.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 120 , December 1990 , pp. 35 - 49
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

References

[1] Andrianov, A. N., Euler products corresponding to Siegel modular forms of genus 2, Russian Math. Surveys, 29 (1974), 45–116.Google Scholar
[2] Harish-Chandra, , Automorphic forms on semisimple Lie groups, Volume 62 of Lecture Notes in Math., Springer-Verlag, 1968.Google Scholar
[3] Kalinin, V. L., Eisenstein series on the symplectic group, Math. USSR Sbornic, 32 (1977), 449–476.Google Scholar
[4] Kohnen, W. and Skoruppa, N.-P., A certain Dirichlet series attached to Siegel modular forms of degree two, Invent. Math. 95 (1989), 541–558.Google Scholar
[5] Maass, Hans, Dirichletsche Reihen und Modulformen zweiten Grades, Acta Arithmetica, 24 (1973), 223–238.CrossRefGoogle Scholar
[6] Maass, Hans, Siegel’s Modular Forms and Dirichlet Series, Volume 216 of Lecture Notes in Math., Springer-Verlag, 1971.Google Scholar
[7] Murase, Atsushi, L-functions attached to jacobi forms of degree n , Part I. 1988, preprint.Google Scholar
[8] Rankin, R. A., Contributions to the theory of Ramanujan’s function τ(n) and similar arithmetical functions I, II, Proc. Cambridge Phil. Soc., 36 (1939), 351–356, 357–372.Google Scholar
[9] Shintani, Takuro, On zeta-functions associated with the vector space of quadratic forms, J. Fac. Sci., Univ. Tokyo Sec. IA, 22 (1975), 25–65.Google Scholar