Journal of Mathematical Sciences

, Volume 133, Issue 6, pp 1622–1626 | Cite as

The Distribution of the Eigenvalues of Hecke Operators

  • E. P. Golubeva


Results of the papers by Serre and by Conrey, Duke, and Farmer on the distribution of the eigenvalues of the Hecke operators Tp on the space of cusp forms of weight k for a fixed p as k increases are refined. Bibliography: 8 titles.


Cusp Form 
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  1. 1.
    J.-P. Serre, “Repartition asymptotique des valeurs propres de l'operateur de Hecke T p,” J. Amer. Math. Soc., 10, No. 1, 75–101 (1997).CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    J. B. Conrey, W. Duke, and D. W. Farmer, “The distribution of the eigenvalues of Hecke operators,” Acta Arithm., 78, No. 4, 405–409 (1997).MathSciNetGoogle Scholar
  3. 3.
    P. Sarnak, “Statistical properties of eigenvalues of the Hecke operators,” in: Analytic Number Theory and Diophantine Problems (Progr. Math., 70), Birkhauser, Boston, Massachusetts (1987), pp. 321–331.Google Scholar
  4. 4.
    P. Michel, “Autour de la conjecture de Sato-Tate pour les sommes de Kloosterman. I,” Invent. Math., 121, 61–78 (1995).CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    R. Livne, “The average distribution of cubic exponential sums,” J. Reine Angew. Math., 375/376, 362–379 (1987).MATHMathSciNetGoogle Scholar
  6. 6.
    E. P. Golubeva, “The distribution of values of the Hecke L-functions at 1,” Zap. Nauchn. Semin. POMI, 314, 15–32 (2004).MATHMathSciNetGoogle Scholar
  7. 7.
    I. M. Vinogradov, The Method of Trigonometric Sums in Number Theory [in Russian], Moscow (1980).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • E. P. Golubeva
    • 1
  1. 1.Bonch-Bruevich State University for TelecommunicationsSt.PetersburgRussia

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