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References (18)
-
D. Bump, S. Friedberg, J. Hoffstein (1990)
Nonvanishing theorems for L-functions of modular forms and their derivativesInventiones mathematicae, 102
-
A. Terras (1985)
Harmonic Analysis on Symmetric Spaces and Applications I -
Y. Choie, W. Kohnen (1997)
Rankin’s method and jacobi formsAbhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 67
-
Daniel Lieman (1994)
Nonvanishing of L-series associated to cubic twists of elliptic curvesAnnals of Mathematics, 140
-
Tadashi Yamazaki (1990)
Rankin-Selberg method for Siegel cusp formsNagoya Mathematical Journal, 120
-
D. Goldfeld, J. Hoffstein (1985)
Eisenstein series of 1/2-integral weight and the mean value of real DirichletL-seriesInventiones mathematicae, 80
-
V. Kalinin (1984)
ANALYTIC PROPERTIES OF THE CONVOLUTION OF SIEGEL MODULAR FORMS OF GENUS nMathematics of The Ussr-sbornik, 48
-
H. Maass (1973)
Dirichletsche Reihen und Modulformen zweiten GradesActa Arithmetica, 24
-
S. Friedberg, J. Hoffstein (1995)
Nonvanishing theorems for automorphic L-functions on GL(2)Annals of Mathematics, 142
-
L. Hörmander (1973)
An introduction to complex analysis in several variables -
D. Bump, S. Friedberg, J. Hoffstein (1990)
Eisenstein series on the metaplectic group and nonvanishing theorems for automorphic L-functions and their derivativesAnnals of Mathematics, 131
-
D. Bump (1998)
Automorphic Forms and Representations: Automorphic Representations -
D. Bump, S. Friedberg, J. Hoffstein (1989)
A nonvanishing theorem for derivatives of automorphic $L$-functions with applications to elliptic curvesBulletin of the American Mathematical Society, 21
-
R. Rankin (1939)
Contributions to the theory of Ramanujan's function Ï„(n) and similar arithmetical functionsMathematical Proceedings of the Cambridge Philosophical Society, 35
-
D. Bump, S. Friedberg, J. Hoffstein (1996)
On some applications of automorphic forms to number theoryBulletin of the American Mathematical Society, 33
-
Helmut Klingen (1990)
Introductory Lectures on Siegel Modular Forms -
Hans Maass (1971)
Siegel's Modular Forms and Dirichlet Series -
R. Langlands (1976)
On the Functional Equations Satisfied by Eisenstein Series
- Publisher
- de Gruyter
- Copyright
- Copyright © 2003 by Walter de Gruyter GmbH & Co. KG
- ISSN
- 0933-7741
- eISSN
- 1435-5337
- DOI
- 10.1515/form.2003.031
- Publisher site
- See Article on Publisher Site
Abstract
Abstract. In this article we study a Rankin-Selberg convolution of two complex variables attached to Siegel modular forms of degree 2. We establish its basic analytic properties, find its singular curves and compute some of its residues. In particular, we show that two known Dirichlet series of Rankin-Selberg type, one introduced by Maass and another by Kohnen and Skoruppa, are obtained as residues from this series of two variables. Furthermore, we define and study a collection of Rankin-Selberg convolutions for Jacobi forms of degree 1. 1991 Mathematics Subject Classification: 11F46, 11F55, 11M41. 1 Introduction À nÁ Let wn ðmÞ ¼ m be the quadratic character of conductor n, p an automorphic representation and Lðw; pÞ the corresponding L-function. The Dirichlet series in two complex variables Dðs; wÞ ¼ P Lðw; p; wn Þ ns n>0 has been the object of some considerable interest. (See for example [3], [4], [5], [8], [9], [16]) The analytic properties of Dðs; wÞ can be used to obtain non-vanishing results for special values and information on the asymptotic properties of Lðw; p; wn Þ. In [2] there is an excellent survey of such results, mostly due to Bump, Friedberg, Goldfeld and Ho¤stein. The
Journal
Forum Mathematicum – de Gruyter
Published: May 21, 2003