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This article is cited in 19 scientific papers (total in 19 papers)
Euler expansions of theta-transforms of Siegel modular forms of degree $n$
A. N. Andrianov
Abstract:
Let $F(Z)$ be a Siegel modular form of degree $n$, weight $k$ and character $\chi$ for the congruence subgroup $\Gamma_0^n(q)$ of the Siegel modular group $\Gamma^n$. Suppose that $F$ is an eigenfunction for all Hecke operators with index relatively prime to $q$. It is proven that for each fixed, symmetric, semi-integral, positive definite matrix $N$ of order $n$ and for each Dirichlet character $\psi$, equal to zero on all prime divisors of $q\operatorname{det}2N$, the Dirichlet series
$$
\sum_{M\in\operatorname{SL}_n(\mathbf Z)\setminus M_n^+(\mathbf Z)}\frac{\psi(\operatorname{det}M)f(MN^tM)}{(\operatorname{det}M)^s},
$$
where $f(N')$ are the Fourier coefficients of $F$ and $M_n^+(\mathbf Z)$ is the set of integral matrices of order $n$ with positive determinant, has an expansion as an Euler product which can be explicitly calculated.
Bibliography: 13 titles.
Received: 17.11.1977
Citation:
A. N. Andrianov, “Euler expansions of theta-transforms of Siegel modular forms of degree $n$”, Mat. Sb. (N.S.), 105(147):3 (1978), 291–341; Math. USSR-Sb., 34:3 (1978), 259–300
Linking options:
https://www.mathnet.ru/eng/sm2523https://doi.org/10.1070/SM1978v034n03ABEH001160 https://www.mathnet.ru/eng/sm/v147/i3/p291
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Abstract page: | 306 | Russian version PDF: | 92 | English version PDF: | 5 | References: | 54 | First page: | 2 |
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