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Mat. Sb. (N.S.), 1978, Volume 106(148), Number 3(7), Pages 323–339 (Mi msb2590)  

This article is cited in 18 scientific papers (total in 18 papers)

On the analytic properties of standard zeta functions of siegel modular forms

A. N. Andrianov, V. L. Kalinin

Abstract: It is proved that standard zeta functions (analogs of the zeta functions of Rankin and Shimura) for holomorphic cusp forms with respect to congruence subgroups of the form
$$ \Gamma_0^n(q)=\{\begin{pmatrix}A&B
C&D\end{pmatrix}\in Sp_n(\mathbf Z);\quad C\equiv0\pmod q\} $$
of the Siegel modular group $Sp_n(\mathbf Z)$ of arbitrary even degree $n$ have a meromorphic continuation. For the case $q=1$, with some additional restrictions, it is proved that the zeta functions are holomorphic except for a finite number of poles, and a functional equation is obtained.
Bibliography: 9 titles.

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English version:
Mathematics of the USSR-Sbornik, 1979, 35:1, 1–17

Bibliographic databases:

UDC: 511.944
MSC: 10D20, 10H10
Received: 16.02.1978

Citation: A. N. Andrianov, V. L. Kalinin, “On the analytic properties of standard zeta functions of siegel modular forms”, Mat. Sb. (N.S.), 106(148):3(7) (1978), 323–339; Math. USSR-Sb., 35:1 (1979), 1–17

Citation in format AMSBIB
\by A.~N.~Andrianov, V.~L.~Kalinin
\paper On the analytic properties of standard zeta functions of siegel modular forms
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 106(148)
\issue 3(7)
\pages 323--339
\jour Math. USSR-Sb.
\yr 1979
\vol 35
\issue 1
\pages 1--17

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    This publication is cited in the following articles:
    1. A. N. Andrianov, “The multiplicative arithmetic or Siegel modular forms”, Russian Math. Surveys, 34:1 (1979), 75–148  mathnet  crossref  mathscinet  zmath
    2. Harris M., “Special Values of Zeta-Functions Attached to Siegel Modular-Forms”, Ann. Sci. Ec. Norm. Super., 14:1 (1981), 77–120  mathscinet  zmath  isi
    3. V. A. Gritsenko, “The action of modular operators on the Fourier–Jacobi coefficients of modular forms”, Math. USSR-Sb., 47:1 (1984), 237–268  mathnet  crossref  mathscinet  zmath
    4. V. L. Kalinin, “Analytic properties of the convolution of Siegel modular forms of genus $n$”, Math. USSR-Sb., 48:1 (1984), 193–200  mathnet  crossref  mathscinet  zmath
    5. V. G. Zhuravlev, “Euler expansions of theta transforms of Siegel modular forms of half-integral weight and their analytic properties”, Math. USSR-Sb., 51:1 (1985), 169–190  mathnet  crossref  mathscinet  zmath
    6. S. Böcherer, “Ein Rationalitätssatz für formale Heckereihen zur Siegelsehen Modulgruppe”, Abh Math Semin Univ Hambg, 56:1 (1986), 35  crossref  mathscinet
    7. Panchishkin A., “Non-Archimedean l-Functions of Siegel and Hilbert Modular-Forms”, Lect. Notes Math., 1471 (1991), 1–154  crossref  mathscinet  isi
    8. Shin-ichiro Mizumoto, “On integrality of Eisenstein liftings”, manuscripta math, 89:1 (1996), 203  crossref  mathscinet  zmath  isi
    9. Panchishkin A., “On the Siegel-Eisenstein Measure and its Applications”, Isr. J. Math., 120:Part b (2000), 467–509  crossref  mathscinet  zmath  isi
    10. S. Böcherer, F.L. Chiera, “Petersson Products of Singular and Almost Singular Theta Series”, manuscripta math, 115:3 (2004), 281  crossref  mathscinet  isi  elib
    11. [Anonymous], “Non-Archimedean l-Functions and Arithmetical Siegel Modular Forms”, Non-Archimedean l-Functions and Arithmetical Siegel Modular Forms, 2nd Augmented Ed, Lecture Notes in Mathematics, 1471, Springer-Verlag Berlin, 2004, 13+  mathscinet  isi
    12. S. Mizumoto, “Congruences for Fourier coefficients of lifted Siegel modular forms I: Eisenstein lifts”, Abh Math Semin Univ Hambg, 75:1 (2005), 97  crossref  mathscinet  zmath
    13. A. A. Panchishkin, “The Maass–Shimura differential operators and congruences between arithmetical Siegel modular forms”, Mosc. Math. J., 5:4 (2005), 883–918  mathnet  mathscinet  zmath
    14. A. A. Panchishkin, “Two Modularity Lifting Conjectures for Families of Siegel Modular Forms”, Math. Notes, 88:4 (2010), 544–551  mathnet  crossref  crossref  mathscinet  isi
    15. Moriyama T., “Generalized Whittaker Functions on Gsp(2, R) Associated with Indefinite Quadratic Forms”, J. Math. Soc. Jpn., 63:4 (2011), 1203–1262  crossref  mathscinet  zmath  isi
    16. Panchishkin A., “Families of Siegel Modular Forms, l-Functions and Modularity Lifting Conjectures”, Isr. J. Math., 185:1 (2011), 343–368  crossref  mathscinet  zmath  isi
    17. H. Katsurada, S. Mizumoto, “Congruences for Hecke eigenvalues of Siegel modular forms”, Abh. Math. Semin. Univ. Hambg, 2012  crossref
    18. File D., “On the Degree Five l-Function for Gsp(4)”, Trans. Am. Math. Soc., 365:12 (2013), 6471–6497  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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