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Group Cohomology and Hecke Operators

  • Michio Kuga
  • Walter Parry
  • Chih-Han Sah
Chapter
Part of the Progress in Mathematics book series (PM, volume 14)

Abstract

Consider the Taylor expansion of the infinite product:
$$t_{n \ge 1}^\pi {(1 - {t^n})^2}{(1 - {t^{11n}})^2} = \sum\limits_{n \ge 1} {{a_n}{t^n}}$$
.

Keywords

Exact Sequence Finite Group Prime Number Spectral Sequence Cohomology Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    W.L. Baily Jr., “The decomposition theorem for V-manifolds,” Amer. J. Math. 78 (1956), 862–888.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    E. Cline, B. Parshall, L. Scott, and W. van der Kallen, “Rational and generic cohomology,” Inv. Math. 39 (1977), 143–163.zbMATHCrossRefGoogle Scholar
  3. [3]
    P. Deligne, “Formes modulai res et representat ions l-adiques,” Sem. Bourbaki, Lect. Notes in Math. 179 (1971), 139–186.CrossRefGoogle Scholar
  4. [4]
    B. Dodson, “Dirichlet series associated to affine manifolds,” Ines is, SUNY Stony Brook, 1976.Google Scholar
  5. [5]
    K. Doi and T. Miyake, “Automorphic forms and number theory,” Kinokuniya Math. Ser. 7 (1976), Kinokuniya, Tokyo.Google Scholar
  6. [6]
    K. Doi and M. Ohta, “On some congruences between cusp forms on T (N),” Mod. Func. of One Var. V., Lect. Notes in Math. 601 (1977), 91–105.MathSciNetCrossRefGoogle Scholar
  7. [7]
    M. Eichler, “Quaternare quadratische Formen und die Riemannsche Vermutung für die Kongruenz-Zetafunktion,” Arohiv Math. 5 (1954), 355–366.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    M. Eichler, “Eine Verallgemeinerung der Abelschen Integrale,” Math. Zeit. 67 (1957), 267–298.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    G. Hochschild and J.-P. Serre, “Cohomology of group extensions,” Trans. Amer. Math. Soc. 74 (1953), 110–134.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    S. Ishida and M. Kuga, Book Review: Modern Number Theory by G. Shimura and Y. Taniyama, Sugaku No Ayumi, 6 (1959), No. 4, (in Japanese).Google Scholar
  11. [11]
    M. Koike, “Congruences between cusp forms and linear representations of the Galois group,” Algebraic Number Theory, Kyoto, 1976, Jap. Soc. for the Promotion of Science, Tokyo, 1977.Google Scholar
  12. [12]
    M. Koike, “Figenvalues of Hecke operators mod p,” (preprint).Google Scholar
  13. [13]
    M. Kuga, “Fiber varieties over a symmetric space whose fibers are abelian varieties,” il, Lect. Notes, Univ. of Chicago, 1963–4.Google Scholar
  14. [14]
    Y. Matsushima and S. Murakami, “On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds,” Ann. of Math. 78 (1963), 365–416.MathSciNetzbMATHCrossRefGoogle Scholar
  15. [15]
    Y. Matsushima and G. Shimura, “On the cohomology groups attached to certain vector valued differential forms on the product of the upper half planes,” Ann. of Math. 78 (1963), 417–449.MathSciNetCrossRefGoogle Scholar
  16. [16]
    Y.H. Rhie and G. Whaples, “Hecke operators in cohomology of groups,” J. Math. Soc. Japan 22 (1970), 431–442.MathSciNetCrossRefGoogle Scholar
  17. [17]
    C.H. Sah, “Automorphisms of finite groups,” J. Alg. 10 (1968), 47–68MathSciNetzbMATHCrossRefGoogle Scholar
  18. [17a]
    C.H. Sah, “Automorphisms of finite groups,” J. Alg. 44 (1977), 573–575.MathSciNetzbMATHCrossRefGoogle Scholar
  19. [18]
    C.H. Sah, “Cohomology of split group extensions,” J. Alg. 29 (1974), 255–302MathSciNetzbMATHCrossRefGoogle Scholar
  20. [18a]
    C.H. Sah, “Cohomology of split group extensions,” J. Alg. 45 (1977), 17–68.MathSciNetzbMATHCrossRefGoogle Scholar
  21. [19]
    J.-P. Serre, “Valeurs propres des operateurs de Hecke modulo l,” Asterisque 24–25 (1975), 109–117.Google Scholar
  22. [20]
    J.-P. Serre, “Formes modulaires et fonctions zeta p-adiques,” Mod. Func. of One Var. III, Lect. Notes in Math. 350 (1973), 191–269.CrossRefGoogle Scholar
  23. [21]
    H. Shimizu, “Automorphic functions, I, II, III,” Fund. Math. (1977–8), Iwanami, Tokyo (in Japanese).Google Scholar
  24. [22]
    G. Shimura, “Sur les integrales attachées aux formes automorphes,” J. Math. Soc. Japan 11 (1952), 291–311.MathSciNetCrossRefGoogle Scholar
  25. [23]
    G. Shimura, “A reciprocity law in nonsolvable extensions,” J. Reine Angew. Math. 221 (1966), 209–220.MathSciNetzbMATHGoogle Scholar
  26. [24]
    G. Shimura, “Introduction to the arithmetic theory of automorphic functions,” Publ. Math. Soc. Japan 11, 1971, Princeton.Google Scholar
  27. [25]
    C.L. Siegel, “Discontinuous groups,” Ann. of Math. 44 (1943), 674–689.MathSciNetzbMATHCrossRefGoogle Scholar
  28. [26]
    H.P.F. Swinnerton-Dyer, “On l-adic representations and congruences for coefficients of modular forms, I, II,” Mod. Func. of One Var. III, V, Lect. Notes in Math. 350 (1973), 1–55MathSciNetCrossRefGoogle Scholar
  29. [26a]
    H.P.F. Swinnerton-Dyer, “On l-adic representations and congruences for coefficients of modular forms, I, II,” Mod. Func. of One Var. III, V, Lect. Notes in Math. 601 (1977), 63–90.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • Michio Kuga
    • 1
  • Walter Parry
    • 1
  • Chih-Han Sah
    • 1
  1. 1.State University of New YorkStony BrookUSA

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