The distribution of the eigenvalues of Hecke operators

J. B. Conrey; W. Duke; D. W. Farmer

Acta Arithmetica (1997)

  • Volume: 78, Issue: 4, page 405-409
  • ISSN: 0065-1036

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J. B. Conrey, W. Duke, and D. W. Farmer. "The distribution of the eigenvalues of Hecke operators." Acta Arithmetica 78.4 (1997): 405-409. <http://eudml.org/doc/206959>.

@article{J1997,
author = {J. B. Conrey, W. Duke, D. W. Farmer},
journal = {Acta Arithmetica},
keywords = {Sato-Tate conjecture; Fourier coefficients of Hecke eigenforms; modular group; uniformly distributed angles; Selberg trace formula},
language = {eng},
number = {4},
pages = {405-409},
title = {The distribution of the eigenvalues of Hecke operators},
url = {http://eudml.org/doc/206959},
volume = {78},
year = {1997},
}

TY - JOUR
AU - J. B. Conrey
AU - W. Duke
AU - D. W. Farmer
TI - The distribution of the eigenvalues of Hecke operators
JO - Acta Arithmetica
PY - 1997
VL - 78
IS - 4
SP - 405
EP - 409
LA - eng
KW - Sato-Tate conjecture; Fourier coefficients of Hecke eigenforms; modular group; uniformly distributed angles; Selberg trace formula
UR - http://eudml.org/doc/206959
ER -

References

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  1. [A] A. Adolphson, On the distribution of angles of Kloosterman sums, J. Reine Angew. Math. 395 (1989), 214-220. Zbl0682.40002
  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. Zbl0183.25503
  3. [K] N. M. Katz, Gauss Sums, Kloosterman Sums, and Monodromy Groups, Ann. of Math. Stud. 116, Princeton, 1988. Zbl0675.14004
  4. [L] R. Livné, The average distribution of cubic exponential sums, J. Reine Angew. Math. 375/376 (1987), 362-379. Zbl0602.10027
  5. [LPS] A. Lubotzky, R. Phillips and P. Sarnak, Ramanujan graphs, Combinatorica 8 (1988), 261-277. Zbl0661.05035
  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. Zbl0219.14013
  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. Zbl0072.08201
  11. [Ser] J.-P. Serre, Abelian l-adic Representations and Elliptic Curves, Benjamin, New York, 1968. 

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