Jacobi-Eisenstein series and p -adic interpolation of symmetric squares of cusp forms

Pavel I. Guerzhoy

Annales de l'institut Fourier (1995)

  • Volume: 45, Issue: 3, page 605-624
  • ISSN: 0373-0956

Abstract

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The aim of this paper is to construct and calculate generating functions connected with special values of symmetric squares of modular forms. The Main Theorem establishes these generating functions to be Jacobi-Eisenstein series i.e. Eisenstein series among Jacobi forms. A theorem on p -adic interpolation of the special values of the symmetric square of a p -ordinary modular form is proved as a corollary of our Main Theorem.

How to cite

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Guerzhoy, Pavel I.. "Jacobi-Eisenstein series and $p$-adic interpolation of symmetric squares of cusp forms." Annales de l'institut Fourier 45.3 (1995): 605-624. <http://eudml.org/doc/75131>.

@article{Guerzhoy1995,
abstract = {The aim of this paper is to construct and calculate generating functions connected with special values of symmetric squares of modular forms. The Main Theorem establishes these generating functions to be Jacobi-Eisenstein series i.e. Eisenstein series among Jacobi forms. A theorem on $p$-adic interpolation of the special values of the symmetric square of a $p$-ordinary modular form is proved as a corollary of our Main Theorem.},
author = {Guerzhoy, Pavel I.},
journal = {Annales de l'institut Fourier},
keywords = {Jacobi forms; Eisenstein series; symmetric square; modular forms; - adic interpolation; Rankin's method; special values},
language = {eng},
number = {3},
pages = {605-624},
publisher = {Association des Annales de l'Institut Fourier},
title = {Jacobi-Eisenstein series and $p$-adic interpolation of symmetric squares of cusp forms},
url = {http://eudml.org/doc/75131},
volume = {45},
year = {1995},
}

TY - JOUR
AU - Guerzhoy, Pavel I.
TI - Jacobi-Eisenstein series and $p$-adic interpolation of symmetric squares of cusp forms
JO - Annales de l'institut Fourier
PY - 1995
PB - Association des Annales de l'Institut Fourier
VL - 45
IS - 3
SP - 605
EP - 624
AB - The aim of this paper is to construct and calculate generating functions connected with special values of symmetric squares of modular forms. The Main Theorem establishes these generating functions to be Jacobi-Eisenstein series i.e. Eisenstein series among Jacobi forms. A theorem on $p$-adic interpolation of the special values of the symmetric square of a $p$-ordinary modular form is proved as a corollary of our Main Theorem.
LA - eng
KW - Jacobi forms; Eisenstein series; symmetric square; modular forms; - adic interpolation; Rankin's method; special values
UR - http://eudml.org/doc/75131
ER -

References

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  1. [1] H. COHEN, Sums involving the values at negative integers of L-functions of quadratic characters, Math. Ann., 217 (1975), 271-285. Zbl0311.10030MR52 #3080
  2. [2] M. EICHLER and D. ZAGIER, The Theory of Jacobi Forms, Progress in Mathematics, vol. 55, Birkhauser, Boston-Basel-Stuttgart, 1985. Zbl0554.10018MR86j:11043
  3. [3] H. HIDA, A p-adic measure attached to the zeta functions associated with two elliptic modular forms 1, Invent. Math., 79 (1985), 159-195. Zbl0573.10020MR86m:11097
  4. [4] Yu. I. MANIN, A.A. PANCHISHKIN, Convolutions of Hecke series and their values at integer points, Mat. Sbornik, 104 (1977), 617-651. Zbl0392.10028
  5. [5] A.A. PANCHISHKIN, Uber nichtarchimedische symmetrische Quadrate von Spitzenformen, Max-Plank-Institut fur Mathematik, Bonn, preprint. 
  6. [6] A.A. PANCHISHKIN, Non-Archimedian ζ-functions, Publishing house of Moscow University, 1988 (in Russian). 
  7. [7] A.A. PANCHISHKIN, Non-Archimedian L-functions of Siegel and Hilbert Modular Forms, Springer Lecture Notes, 1471, Springer Verlag, 1991. Zbl0732.11026MR93a:11044
  8. [8] G. SHIMURA, On modular forms of half-integral weight, Ann. of Math., 97 (1973), 440-481. Zbl0266.10022MR48 #10989
  9. [9] D. ZAGIER, Periods of modular forms and Jacobi theta-functions, Invent. Math., 104 (1991), 449-465. Zbl0742.11029MR92e:11052
  10. [10] D. ZAGIER, Modular forms whose Fourier coefficients involve zeta-functions of quadratic fields, in Modular Functions of One Variable 4, Springer Lecture Notes 627, 105-169, Springer Verlag, 1977. Zbl0372.10017MR58 #5525

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