ArticleOriginal scientific text

Title

Zeros of Hecke L-functions associated with cusp forms

Authors 1

Affiliations

  1. Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, California 94720, U.S.A.

Bibliography

  1. E. Bombieri and D. A. Hejhal, On the distribution of zeros of linear combinations of Euler products, preprint, 1993.
  2. P. Deligne, Formes modulaires et représentations l-adiques, Sém. Bourbaki, 1968/69, exposés 355.
  3. P. Deligne, La conjecture de Weil, I, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 273-307.
  4. W. Duke and H. Iwaniec, Bilinear forms in the Fourier coefficients of half-integral weight cusp forms and sums over primes, Math. Ann. 286 (1990), 783-802.
  5. W. Duke, J. Friedlander and H. Iwaniec, Bound for automorphic L-functions, Invent. Math. 112 (1993), 1-8.
  6. D. Farmer, Mean value of Dirichlet series associated with holomorphic cusp forms, J. Number Theory, to appear.
  7. A. Good, Approximative Funktionalgleichungen und Mittelwertsätze für Dirichletreihen, die Spitzenformen assoziiert sind, Comment. Math. Helv. 50 (1975), 327-361.
  8. A. Good, Beiträge zur Theorie der Dirichletreihen, die Spitzenformen zugeordnet sind, J. Number Theory 13 (1981), 18-65.
  9. G. H. Hardy, Note on Ramanujan's function τ(n), Proc. Cambridge Philos. Soc. 23 (1927), 675-680.
  10. E. Hecke, Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung, Math. Ann. 112 (1936), 664-699.
  11. E. Hecke, Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung, Math. Ann. 114 (1937), 1-28.
  12. J. L. Hafner, Explicit estimates in the arithmetic theory of cusp forms and Poincaré series, Math. Ann. 264 (1983), 9-20.
  13. J. L. Hafner, On the zeros (à la Selberg) of Dirichlet series attached to certain cusp forms, in: Topics in Analytic Number Theory, Austin, 1985, 127-164.
  14. M. Jutila, Zeros of the zeta-function near the critical line, in: Studies in Pure Mathematics to the Memory of Paul Turán, Birkhäuser, Basel, 1982, 385-394.
  15. C. G. Lekkerkerker, On the zeros of a class of Dirichlet series, Dissertation, Utrecht, 1955.
  16. H. L. Montgomery and R. C. Vaughan, Hilbert's inequality, J. London Math. Soc. 8 (1974), 73-82.
  17. C. J. Moreno, Explicit formulas in the theory of automorphic forms, in: Lecture Notes in Math. 626, Springer, 1977, 73-216.
  18. R. A. Rankin, Contributions to the theory of Ramanujan's function τ(n) and similar arithmetic functions, Proc. Cambridge Philos. Soc. 35 (1939), 357-372.
  19. A. Selberg, On the zeros of Riemann's zeta-function, in: Collected Papers, Vol. I, Springer, 1989, 85-141.
  20. A. Selberg, Contributions to the theory of the Riemann zeta-function, in: Collected Papers, Vol. I, Springer, 1989, 214-280.
  21. E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford, 1951.
  22. E. C. Titchmarsh, The Theory of Functions, Oxford, 1952
Pages:
139-158
Main language of publication
English
Received
1994-06-06
Accepted
1994-10-28
Published
1995
Exact and natural sciences