Zeros of Hecke L-functions associated with cusp forms

• Autorzy: Wenzhi Luo
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 71
• Numer: 2
• Strony: 139-158

Daty

wydano

1995

otrzymano

1994-06-06

poprawiono

1994-10-28

Twórcy

autor

Wenzhi Luo

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

Bibliografia

• [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