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Hecke operators and Siegel modular forms

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Articles (72)

  • Die Primzahlen in der Theorie der Siegelschen Modulfunktionen PDF [1056]
  • Hans Maa{ss}
  • Math. Ann.
  • Volume: 124
  • Year: 1951
  • Pages: 87-122
  • MR number: 0047075
  • Zur Operatorentheorie der Modulformen $n$-ten Grades PDF [448]
  • Max Koecher
  • Math. Ann.
  • Volume: 130
  • Year: 1956
  • Pages: 351-385
  • MR number: 0077567
  • On modular correspondences for $Sp(n,,Z)$ and their congruence relations [463]
  • Goro Shimura
  • Proc. Nat. Acad. Sci. USA
  • Volume: 49
  • Year: 1963
  • Pages: 824-828
  • MR number: 0157009
  • Rationality of multiple Hecke series of the full linear group and Shimura's hypothesis on Hecke series of the Symplectic group [563]
  • Anatoli Andrianov
  • Doklady Akad. Nauk SSSR (N.S.)
  • Volume: 183
  • Year: 1968
  • Pages: 9-11
  • MR number: 0241365
  • Rationality theorems for Hecke series and Zeta functions of the groups ${rm GL}sb{n}$ and ${rm Sp}sb{n}$ over local fields [564]
  • Anatoli Andrianov
  • Izv. Akad. Nauk SSSR Ser. Mat.
  • Volume: 33
  • Year: 1969
  • Pages: 466-505
  • MR number: 0262168
  • Spherical functions for ${rm GL}sb{n}$ over local fields, and the summation of Hecke series. [570]
  • Anatoli Andrianov
  • Mat. Sb. (N.S.)
  • Volume: 83(125)
  • Year: 1970
  • Pages: 429-451
  • MR number: 0282982
  • Dirichlet series with Euler product in the theory of Siegel modular forms of genus two [341]
  • Anatoli Andrianov
  • Proc. Steklov Inst. Math.
  • Volume: 112
  • Year: 1971
  • Pages: 70-93
  • MR number: 0340178
  • On Fourier coefficients of Siegel modular forms of degree two [339]
  • Erik Lippa
  • Bull. Amer. Math. Soc.
  • Volume: 79
  • Year: 1973
  • Pages: 1242-1246
  • MR number: 0325542
  • Siegel forms and zeta-functions [348]
  • Anatoli Andrianov
  • Proc. Steklov Inst. Math.
  • Volume: 132
  • Year: 1973
  • Pages: 132-136
  • MR number: 0345911
  • Euler products that correspond to Siegel's modular forms of genus $2$ [372]
  • Anatoli Andrianov
  • Uspehi Mat. Nauk
  • Volume: 29
  • Year: 1974
  • Pages: 43-110
  • MR number: 0432552
  • Siegel modular forms of degree two: Hecke eigenforms PDF [349]
  • Erik Lippa
  • Math. Ann.
  • Volume: 209
  • Year: 1974
  • Pages: 195-200
  • MR number: 0345912
  • The Siegel operator and Hecke operators. (Russian) [1072]
  • N. Zarkovskaja
  • Funct. Anal. Appl.
  • Volume: 8
  • Year: 1974
  • Pages: 113-120
  • MR number: 0349589
  • On Fourier coefficients of Siegel modular forms of degree two [360]
  • Erik Lippa
  • Amer. J. Math.
  • Volume: 97
  • Year: 1975
  • Pages: 829-846
  • MR number: 0384704
  • The connection between the eigenvalues of Hecke operators and the Fourier coefficients of eigenfunctions for Siegel modular forms of genus $n$ [359]
  • N. Zarkovskaja
  • Mat. Sb. (N.S.)
  • Volume: 96 (138)
  • Year: 1975
  • Pages: 584-593, 646
  • MR number: 0379383
  • Zeta functions and the Siegel modular forms [365]
  • Anatoli Andrianov
  • Lie groups and their representations (Proc. Summer School, Bolyai János Math. Soc., Budapest, 1971)
  • Year: 1975
  • Pages: 9-20
  • MR number: 0404149
  • Euler products for congruence subgroups of the Siegel group of genus 2 [367]
  • Sergei Evdokimov
  • Mat. Sb. (N.S.)
  • Volume: 99 (141)
  • Year: 1976
  • Pages: 483-513
  • MR number: 0414492
  • Hecke eigenforms of degree two: Dirichlet series and Euler products PDF [395]
  • Erik Lippa
  • Math. Ann.
  • Volume: 220
  • Year: 1976
  • Pages: 263-271
  • MR number: 0480359
  • On zeta-functions of Rankin type associated with Siegel modular forms [399]
  • Anatoli Andrianov
  • Springer Lecture Notes in Mathematics
  • Volume: 627
  • Year: 1977
  • Pages: 325-338
  • MR number: 0491514
  • Relations between the Hecke rings of the groups ${rm Sp}sb{n}$ and ${rm SL}sb{n}$ [373]
  • Anatoli Andrianov
  • Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI)
  • Volume: 71
  • Year: 1977
  • Pages: 5-15, 282
  • MR number: 0498396
  • Symmetric squares of the zeta functions for a principal congruence subgroup of the Siegel group of genus $2$ [402]
  • Valeri Gritsenko
  • Mat. Sb. (N.S.)
  • Volume: 104(146)
  • Year: 1977
  • Pages: 22-41, 175
  • MR number: 0563062
  • The expansion of Hecke polynomials for the symplectic group of genus $n$ [876]
  • Anatoli Andrianov
  • Mat. Sb. (N.S.)
  • Volume: 104 (146)
  • Year: 1977
  • Pages: 390-427, 511
  • MR number: 0562510
  • Analytic continuation of symmetric squares [403]
  • Valeri Gritsenko
  • Mat. Sb. (N.S.)
  • Volume: 107(149)
  • Year: 1978
  • Pages: 323-346, 463
  • MR number: 0515736
  • Analytic properties of standard zeta-functions of Siegel modular forms [401]
  • Anatoli Andrianov; V. Kalinin
  • Mat. Sb. (N.S.)
  • Volume: 106(148)
  • Year: 1978
  • Pages: 323-339, 495
  • MR number: 0506044
  • Euler expansions of the theta-transform of Siegel modular forms of genus $n$ [375]
  • Anatoli Andrianov
  • Mat. Sb. (N.S.)
  • Volume: 105(147)
  • Year: 1978
  • Pages: 291-341, 463
  • MR number: 0563060
  • Dirichlet series corresponding to Siegel modular forms of degree $2$, level $N$ [434]
  • Isao Matsuda Makino
  • Sci. Papers College Gen. Ed. Univ. Tokyo
  • Volume: 28
  • Year: 1978
  • Pages: 21-49
  • MR number: 0498402
  • Correction to my article: "Dirichlet series corresponding to Siegel modular forms of degree $2$, level $N$" [435]
  • Isao Matsuda Makino
  • Sci. Papers College Gen. Ed. Univ. Tokyo
  • Volume: 29
  • Year: 1979
  • Pages: 29-30
  • MR number: 0541086
  • A basis composed of eigenfunctions of Hecke operators in the theory of modular forms of genus $n$ [368]
  • Sergei Evdokimov
  • Mat. Sb. (N.S.)
  • Volume: 115(157)
  • Year: 1981
  • Pages: 337-363, 495
  • MR number: 0628215
  • Letter to the editors: "A basis composed of eigenfunctions of Hecke operators in the theory of modular forms of genus $n$" [369]
  • Sergei Evdokimov
  • Mat. Sb. (N.S.)
  • Volume: 116(158)
  • Year: 1981
  • Pages: 603
  • MR number: 0665861
  • On Eisenstein series for Siegel modular groups [420]
  • Nobushige Kurokawa
  • Proc. Japan Acad. Ser. A Math. Sci
  • Volume: 57
  • Year: 1981
  • Pages: 51-55
  • MR number: 0608391
  • On Eisenstein series for Siegel modular groups. II [421]
  • Nobushige Kurokawa
  • Proc. Japan Acad. Ser. A Math. Sci
  • Volume: 57
  • Year: 1981
  • Pages: 315-320
  • MR number: 0628118
  • On Eisenstein series of degree two [422]
  • Nobushige Kurokawa; Shin-ichiro Mizumoto
  • Proc. Japan Acad. Ser. A Math. Sci
  • Volume: 57
  • Year: 1981
  • Pages: 134-139
  • MR number: 0605300
  • The rationality of holomorphic Eisenstein series PDF [426]
  • Michael Harris
  • Invent. Math.
  • Volume: 63
  • Year: 1981
  • Pages: 305-310
  • MR number: 0610541
  • Recursive relations in the theory of Hecke operators [297]
  • Valeri Gritsenko
  • Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI)
  • Volume: 125
  • Year: 1983
  • Pages: 65-73
  • MR number: 0697767
  • Hecke rings for a covering of the symplectic group [298]
  • V. Zhuravlev
  • Math. USSR-Sb.
  • Volume: 49
  • Year: 1984
  • Pages: 379-399
  • MR number: 0708003
  • The effect of modular operators on the Fourier-Jacobi coefficients of modular forms [296]
  • Valeri Gritsenko
  • Math. USSR-Sb.
  • Volume: 47
  • Year: 1984
  • Pages: 237-268
  • MR number: 0675196
  • Representations of an even zeta function by theta series [83]
  • Anatoli Andrianov
  • Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI)
  • Volume: 134
  • Year: 1984
  • Pages: 5-14
  • MR number: 0741851
  • Action of an irregular Hecke operator with number $p$ on the theta series of a quadratic form [89]
  • Sergei Evdokimov
  • Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI)
  • Volume: 144
  • Year: 1985
  • Pages: 68-71, 175
  • MR number: 0787414
  • Factorization of Hecke polynomials in a parabolic extension. (Spanish) [110]
  • Jorge Estrada Sarlabous; Valeri Gritsenko
  • Cienc. Mat. (Havana)
  • Volume: 6
  • Year: 1985
  • Pages: 56-69
  • MR number: 0850919
  • Hecke operators for the principal congruence subgroup of the group ${rm Sp}(n, Z)$ [302]
  • Alexander Nenashev
  • J. Soviet Math.
  • Volume: 43
  • Year: 1988
  • Pages: 2592-2596
  • MR number: 0859528
  • Multiplicative properties of the Fourier coefficients of Siegel modular forms for the principal congruence subgroups of the group $mathrm{Sp}(n,mathbf{Z})$ [121]
  • Alexander Nenashev
  • Math. USSR-Sb.
  • Volume: 60
  • Year: 1988
  • Pages: 237-254
  • MR number: 0882836
  • Prolongation of Siegel modular forms to the Siegel-Satake half plane [305]
  • N. Zharkovskaya
  • J. Soviet Math.
  • Volume: 52
  • Year: 1990
  • Pages: 3069-3077
  • MR number: 0906848
  • Certain $L$-series of Ranking [Rankin]-Selberg type associated to Siegel modular forms of degree $g$ PDF [560]
  • Winfried Kohnen
  • Math. Ann.
  • Volume: 288
  • Year: 1990
  • Pages: 697-711
  • MR number: 1081271
  • Factorization of Hecke polynomials of classical groups [940]
  • Valeri Gritsenko
  • Math. USSR-Sb.
  • Volume: 65
  • Year: 1990
  • Pages: 333-356
  • MR number: 0976515
  • Hecke operators with respect to the modular group of quaternions [500]
  • Aloys Krieg
  • Abh. Math. Sem. Univ. Hamburg
  • Volume: 60
  • Year: 1990
  • Pages: 71-85
  • MR number: 1087119
  • The Maaß space and Hecke operators PDF [499]
  • Aloys Krieg
  • Math. Z.
  • Volume: 204
  • Year: 1990
  • Pages: 527-550
  • MR number: 1062134
  • A generalization of Gauss sums and its applications to Siegel modular forms and $L$-functions associated with the vector space of quadratic forms [189]
  • Hiroshi Saito
  • J. Reine Angew. Math.
  • Volume: 416
  • Year: 1991
  • Pages: 91-142
  • MR number: 1099947
  • On the Shimura correspondence for ${rm GSp}(4)$ PDF [331]
  • Solomon Friedberg; Shek-Tung Wong
  • Math. Ann.
  • Volume: 290
  • Year: 1991
  • Pages: 183-207
  • MR number: 1107667
  • A correspondence between Hecke rings ${scr L}sp nsb 0(q)$ and ${scr D}sp n$ [968]
  • Jae Myung Chung; Myung-Hwan Kim
  • Bull. Korean Math. Soc.
  • Volume: 29
  • Year: 1992
  • Pages: 101-116
  • MR number: 1157250
  • Dirichlet series involving special values of Rankin convolutions attached to Siegel modular forms [571]
  • Winfried Kohnen
  • Abh. Math. Sem. Univ. Hamburg
  • Volume: 62
  • Year: 1992
  • Pages: 163-167
  • MR number: 1182846
  • Invariance of the space of theta-series under theta operators [969]
  • Myung-Hwan Kim
  • Bull. Korean Math. Soc.
  • Volume: 29
  • Year: 1992
  • Pages: 245-256
  • MR number: 1180618
  • Arithmetic of half integral weight theta-series [970]
  • Myung-Hwan Kim
  • Acta Arith.
  • Volume: 63
  • Year: 1993
  • Pages: 157-181
  • MR number: 1206082
  • Jacobi forms and Siegel modular forms: recent results and problems [575]
  • Winfried Kohnen
  • Enseign. Math.
  • Volume: 39
  • Year: 1993
  • Pages: 121-136
  • MR number: 1225259
  • The cusp forms of weight $3$ on $Gammasb 2(2,4,8)$ [1027]
  • Bert van Geemen; Duco van Straten
  • Math. Comp.
  • Volume: 61
  • Year: 1993
  • Pages: 849-872
  • MR number: 1181333
  • A space of Siegel modular forms closed under the action of Hecke operators [271]
  • Yoshiyuki Kitaoka
  • Proc. Japan Acad. Ser. A Math. Sci
  • Volume: 70
  • Year: 1994
  • Pages: 194-197
  • MR number: 1291181
  • A note on Hecke eigenforms [1005]
  • Kalyan Chakraborty; B. Ramakrishnan
  • Arch. Math.
  • Volume: 63
  • Year: 1994
  • Pages: 509-516
  • MR number: 1300750
  • Nearly holomorphic Eisenstein liftings [704]
  • Shin-ichiro Mizumoto
  • Abh. Math. Sem. Univ. Hamburg
  • Volume: 67
  • Year: 1997
  • Pages: 173-194
  • MR number: 1481535
  • Siegel Eisenstein series and Hecke operators [703]
  • Riccardo Salvati Manni
  • Abh. Math. Sem. Univ. Hamburg
  • Volume: 67
  • Year: 1997
  • Pages: 255-267
  • MR number: 1481541
  • Nearly holomorphic Eisenstein liftings. (Japanese) [850]
  • Shin-ichiro Mizumoto
  • Surikaisekikenkyusho Kokyuroku
  • Volume: 1002
  • Year: 1997
  • Pages: 82-88
  • MR number: 1622819
  • Pseudodifferential operators and Hecke operators [1106]
  • Youngju Choie
  • Appl. Math. Lett.
  • Volume: 11
  • Year: 1998
  • Pages: 29-34
  • MR number: 1638733
  • On explicit lifts of cusp forms from ${rm GL}sb m$ to classical groups [202]
  • David Ginzburg; Stephen Rallis; David Soudry
  • Ann. of Math.
  • Volume: 150
  • Year: 1999
  • Pages: 807-866
  • MR number: 1740991
  • On Hecke eigenforms of degree $n$ [672]
  • Stefan Breulmann; Winfried Kohnen
  • Abh. Math. Sem. Univ. Hamburg
  • Volume: 70
  • Year: 2000
  • Pages: 119-123
  • MR number: 1809540
  • On the coincidence of Hecke-eigenforms [673]
  • Hidenori Katsurada
  • Abh. Math. Sem. Univ. Hamburg
  • Volume: 70
  • Year: 2000
  • Pages: 77-83
  • MR number: 1809535
  • Singular Hecke-Shimura rings and Hecke operators on Siegel modular forms [886]
  • Anatoli Andrianov
  • St. Petersburg Math. J.
  • Volume: 11
  • Year: 2000
  • Pages: 931-987
  • MR number: 1746068
  • Singular Frobenius operators on Siegel modular forms with characters, and zeta functions [665]
  • Anatoli Andrianov; Alexei Panchishkin
  • St. Petersburg Math. J.
  • Volume: 12
  • Year: 2001
  • Pages: 233-257
  • MR number: 1768138
  • Siegel modular forms and Hecke operators in degree 2 [631]
  • James Hafner; Lynne Walling
  • Number theory for the millennium, II (Urbana, IL, 2000)
  • Year: 2002
  • Pages: 117-148
  • MR number: 1956248
  • Theta-transforms and even zeta functions of Siegel modular forms [638]
  • Anatoli Andrianov
  • Acta Arith.
  • Volume: 101
  • Year: 2002
  • Pages: 231-245
  • MR number: 1875842
  • Explicit action of Hecke operators on Siegel modular forms [1110]
  • James Hafner; Lynne Walling
  • J. Number Theory
  • Volume: 93
  • Year: 2002
  • Pages: 34-57
  • MR number: 1892929
  • A remark on the coincidence of Hecke-eigenforms PDF [609]
  • Hidenori Katsurada
  • Comment. Math. Univ. St. Paul
  • Volume: 52
  • Year: 2003
  • Pages: 47-54
  • MR number: 1993951
  • A weak multiplicity-one theorem for Siegel modular forms [597]
  • Rudolf Scharlau; Lynne Walling
  • Pacific J. Math.
  • Volume: 211
  • Year: 2003
  • Pages: 369-374
  • MR number: 2015741
  • On diagonalization of singular Frobenius operators on Siegel modular forms [889]
  • Anatoli Andrianov
  • Amer. J. Math.
  • Volume: 125
  • Year: 2003
  • Pages: 139-165
  • MR number: 1953520
  • Iwahori-spherical representations of ${rm GSp}(4)$ and Siegel modular forms of degree 2 with square-free level [717]
  • Ralf Schmidt
  • J. Math. Soc. Japan
  • Volume: 57
  • Year: 2005
  • Pages: 259-293
  • MR number: 2114732
  • Action of Hecke operators on Siegel theta series. I. [1291]
  • Lynne Walling
  • Int. J. Number Theory
  • Volume: 2
  • Year: 2006
  • Pages: 169--186
  • MR number: 2240221

Preprints (1)

  • Computing the Satake p-parameters of Siegel modular forms [1329]
  • Nathan Ryan
  • pdf
  • Year: 2004
  • Pages: 25 pp