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This article is cited in 82 scientific papers (total in 82 papers)
Euler products corresponding to Siegel modular froms of genus 2
A. N. Andrianov
Abstract:
In this article we construct a theory of Dirichlet series with Euler product expansions corresponding to analytic automorphic forms for the integral symplectic group in genus 2; in Chapter 2 we establish a connection between the eigenvalues of the Hecke operators on the spaces of such forms with the Fourier coefficients of the eigenfunctions (Theorem 2.4.1); in Chapter 3 we demonstrate the possibility of analytic continuation to the entire complex plane and derive a functional equation for Euler products corresponding to the eigenfunctions of the Hecke operators (Theorem 3.1.1). Chapter 1 contains a survey of the present state of the theory of Euler products for Siegel modular forms of arbitrary genus $n$, including a sketch of the classical Hecke theory for the case $n=1$.
Received: 16.10.1973
Citation:
A. N. Andrianov, “Euler products corresponding to Siegel modular froms of genus 2”, Uspekhi Mat. Nauk, 29:3(177) (1974), 43–110; Russian Math. Surveys, 29:3 (1974), 45–116
Linking options:
https://www.mathnet.ru/eng/rm4375https://doi.org/10.1070/RM1974v029n03ABEH001285 https://www.mathnet.ru/eng/rm/v29/i3/p43
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Abstract page: | 947 | Russian version PDF: | 353 | English version PDF: | 25 | References: | 52 | First page: | 3 |
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