On Ramanujan congruences between special values of Hecke and Dirichlet L-functions

P. Guerzhoy

Acta Arithmetica (1997)

  • Volume: 81, Issue: 1, page 11-23
  • ISSN: 0065-1036

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P. Guerzhoy. "On Ramanujan congruences between special values of Hecke and Dirichlet L-functions." Acta Arithmetica 81.1 (1997): 11-23. <http://eudml.org/doc/207050>.

@article{P1997,
author = {P. Guerzhoy},
journal = {Acta Arithmetica},
keywords = {Ramanujan congruence; congruences between special values of -functions of modular forms; Fourier coefficients},
language = {eng},
number = {1},
pages = {11-23},
title = {On Ramanujan congruences between special values of Hecke and Dirichlet L-functions},
url = {http://eudml.org/doc/207050},
volume = {81},
year = {1997},
}

TY - JOUR
AU - P. Guerzhoy
TI - On Ramanujan congruences between special values of Hecke and Dirichlet L-functions
JO - Acta Arithmetica
PY - 1997
VL - 81
IS - 1
SP - 11
EP - 23
LA - eng
KW - Ramanujan congruence; congruences between special values of -functions of modular forms; Fourier coefficients
UR - http://eudml.org/doc/207050
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. Zbl0311.10030
  2. [2] B. Datskovsky and P. Guerzhoy, On Ramanujan congruences for modular forms of higher weight, Proc. Amer. Math. Soc., to appear. Zbl0864.11023
  3. [3] P. Deligne and J.-P. Serre, Formes modulaires de poids 1, Ann. Sci. Ecole Norm. Sup. 7 (1974), 507-530. Zbl0321.10026
  4. [4] P. I. Gerzhoĭ and A. A. Panchishkin, Finiteness criterion for the number of rational points on twisted Weil elliptic curves, Zap. Nauch. Sem. LOMI 160 (1987), 41-53. Zbl0679.14013
  5. [5] N. M. Katz, p-adic continuation of real analytic Eisenstein series, Ann. of Math. 104 (1976), 459-571. 
  6. [6] N. Koblitz, Congruences for periods of modular forms, Duke Math. J. 54 (1987), 361-373. Zbl0628.10032
  7. [7] N. Koblitz, p-adic congruences and modular forms of half integer weight, Math. Ann. 274 (1986), 199-220. Zbl0571.10030
  8. [8] W. Kohnen, A simple remark on eigenvalues of Hecke operators on Siegel modular forms, Abh. Math. Sem. Univ. Hamburg 57 (1987), 33-36. Zbl0641.10022
  9. [9] Yu. I. Manin, Periods of parabolic forms and p-adic Hecke series, Mat. Sb. 92 (1973), 378-401 (in Russian). Zbl0293.14007
  10. [10] K. A. Ribet, Congruence relations between modular forms, in: Proceedings of the International Congress of Mathematicians (Warsaw, 1983), PWN, Warszawa, 1984, 503-514. Zbl0575.10024
  11. [11] G. Shimura, The special values of the zeta-functions associated with cusp forms, Comm. Pure Appl. Math. 29 (1976), 783-804. Zbl0348.10015
  12. [12] H. P. F. Swinnerton-Dyer, On l-adic representations and congruences for coefficients of modular forms, in: Modular Functions of One Variable III, Lecture Notes in Math. 350, Springer, 1973, 1-55. 
  13. [13] H. P. F. Swinnerton-Dyer, Congruence properties of τ(n), in: Ramanujan Revisited, Proceedings of the Centenary Conference, Academic Press, 1988, 289-311. 

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