ArticleOriginal scientific text

Title

The distribution of the eigenvalues of Hecke operators

Authors 1, 2, 3

Affiliations

  1. Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078, U.S.A.
  2. Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, U.S.A.
  3. Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania, 17837 U.S.A.

Bibliography

  1. [A] A. Adolphson, On the distribution of angles of Kloosterman sums, J. Reine Angew. Math. 395 (1989), 214-220.
  2. [B] B. J. Birch, How the number of points of an elliptic curve over a fixed prime field varies, J. London Math. Soc. 43 (1968), 57-60.
  3. [K] N. M. Katz, Gauss Sums, Kloosterman Sums, and Monodromy Groups, Ann. of Math. Stud. 116, Princeton, 1988.
  4. [L] R. Livné, The average distribution of cubic exponential sums, J. Reine Angew. Math. 375/376 (1987), 362-379.
  5. [LPS] A. Lubotzky, R. Phillips and P. Sarnak, Ramanujan graphs, Combinatorica 8 (1988), 261-277.
  6. [Mic] P. Michel, Autour de la conjecture de Sato-Tate pour les sommes de Kloosterman I, Invent. Math. 121 (1995), 61-78.
  7. [Mur] V. K. Murty, On the Sato-Tate conjecture, in: Number Theory Related to Fermat's Last Theorem, Progr. Math. 26, Birkhäuser, Boston, 1981, 195-205.
  8. [Ogg] A. P. Ogg, A remark on the Sato-Tate conjecture, Invent. Math. 9 (1970), 198-200.
  9. [Sar] P. Sarnak, Statistical properties of eigenvalues of the Hecke operators, in: Analytic Number Theory and Diophantine Problems (Stillwater, OK, 1984), Progr. Math. 70, Birkhäuser, Boston, 1987, 321-331.
  10. [Sel] A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. B 20 (1956), 47-87; reprinted in: Collected Papers, Vol. I, Springer, Berlin, 1989, 423-463.
  11. [Ser] J.-P. Serre, Abelian l-adic Representations and Elliptic Curves, Benjamin, New York, 1968.
Pages:
405-409
Main language of publication
English
Received
1996-08-20
Published
1997
Exact and natural sciences