Une interprétation des congruences relatives à la fonction τ de Ramanujan

Jean-Pierre Serre

Séminaire Delange-Pisot-Poitou. Théorie des nombres (1967-1968)

  • Volume: 9, Issue: 1, page 1-17

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Serre, Jean-Pierre. "Une interprétation des congruences relatives à la fonction $\tau $ de Ramanujan." Séminaire Delange-Pisot-Poitou. Théorie des nombres 9.1 (1967-1968): 1-17. <http://eudml.org/doc/110695>.

@article{Serre1967-1968,
author = {Serre, Jean-Pierre},
journal = {Séminaire Delange-Pisot-Poitou. Théorie des nombres},
keywords = {number theory},
language = {fre},
number = {1},
pages = {1-17},
publisher = {Secrétariat mathématique},
title = {Une interprétation des congruences relatives à la fonction $\tau $ de Ramanujan},
url = {http://eudml.org/doc/110695},
volume = {9},
year = {1967-1968},
}

TY - JOUR
AU - Serre, Jean-Pierre
TI - Une interprétation des congruences relatives à la fonction $\tau $ de Ramanujan
JO - Séminaire Delange-Pisot-Poitou. Théorie des nombres
PY - 1967-1968
PB - Secrétariat mathématique
VL - 9
IS - 1
SP - 1
EP - 17
LA - fre
KW - number theory
UR - http://eudml.org/doc/110695
ER -

References

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  2. [2] Bambah ( R.P.). - Two congruence properties of Ramanujan's function τ(n) , J. London math. Soc., t. 21, 1946, p. 91-93. Zbl0060.10204
  3. [3] Davenport ( H.) und Hasse ( H.). - Die Nullstelle der Kongruenzzetafunktionen in gewissen zyklischen Fällen, J. für reine und angew. Math. [J. Crelle], t. 172, 1935, p. 151-182. JFM60.0913.01
  4. [4] Eichler ( M.). - Quaternäre quadratische Formen und die Riemannsche Vermutung für die Kongruenzzetafunktion, Archiv der Math., t. 5, 1954, p. 355-366. Zbl0059.03804MR63406
  5. [5] Hardy ( G.H.). - Ramanujan (Twelve lectures on subjects suggested by his life and his work). - Cambridge University Press, 1940 [Reprint : New York, Chelsea publishing Company, 1959]. Zbl0025.10505
  6. [6] Hecke ( E. ) . - Mathematische Werke. - Göttingen, Vandenhoeck und Ruprecht, 1959. Zbl0092.00102MR104550
  7. [7] Igusa ( J.). - Kroneckerian model of fields of elliptic modular functions, Amer. J. of Math., t. 81, 1959, p. 561-577. Zbl0093.04502MR108498
  8. [8] Ihara ( Y.). - Hecke polynomials as congruence ζ functions in elliptic modular case, Annals of Math., Series 2, t. 85, 1967, p. 267-295. Zbl0181.36501
  9. [9] Kuga ( M.). - Fiber varieties over a symmetric space whose fibers are abelian varieties [Notes polycopiées], University of Chicago, 1963/64. 
  10. [10] Kuga ( M.) and Shimura ( G.). - On the zeta function of a fibre variety whose fibres are abelian varieties, Annals of Math., Series 2, t. 82, 1965, p. 478-539. Zbl0166.16801MR184942
  11. [11] Lehmer ( D.H.). - Ramanujan's function τ(n) , Duke math. J., t. 10, 1943, p. 483-492. Zbl0060.10402
  12. [12] Lehmer ( D.H.). - The vanishing of Ramanujan's function τ(n) , Duke math. J., t. 14, 1947, p. 429-433. Zbl0029.34502
  13. [13] Lehmer ( D.H.). - Notes on some arithmetical properties of elliptic modular functions [Notes polycopiées, Berkeley, non datées]. 
  14. [14] Mordell ( L.J.). - On Mr Ramanujan's empirical expressions of modular functions, Proc. Cambridge phil. Soc., t. 19, 1917, p. 117-124. Zbl46.0605.01JFM46.0605.01
  15. [15] Ramanathan ( K.G.). - Congruence properties of Ramanujan's function τ(n) , (II), J. Indian math. Soc., t. 9, 1945, p. 55-59. Zbl0063.06404
  16. [16] Ramanujan ( S.). - On certain arithmetical functions, Trans. Cambridge phil. Soc., t. 22, 1916, p. 159-184. 
  17. [17] Serre ( J.-P.). - Abelian l-adic representations and elliptic curves. - New York, Benjamin, 1968. Zbl0186.25701MR263823
  18. [18] Shimura ( G.). - Correspondances modulaires et les fonctions zêtas des courbes algébriques, J. Math. Soc. Japan, t. 10, 1958, p. 1-28. Zbl0081.07603MR95173
  19. [19] Shimura ( G.). - A reciprocity law in non-solvable extensions, J. für reine und angew. Math. [J. Crelle], t. 221, 1966, p. 209-220. Zbl0144.04204MR188198
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  21. [21] Wilton ( J.R.). - Congruence properties of Ramanujan's function τ(n) , Proc. London math. Soc., t. 31, 1930, p. 1-10. JFM56.0874.02

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