Zeros of Hecke L-functions associated with cusp forms

Wenzhi Luo

Acta Arithmetica (1995)

  • Volume: 71, Issue: 2, page 139-158
  • ISSN: 0065-1036

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Wenzhi Luo. "Zeros of Hecke L-functions associated with cusp forms." Acta Arithmetica 71.2 (1995): 139-158. <http://eudml.org/doc/206764>.

@article{WenzhiLuo1995,
author = {Wenzhi Luo},
journal = {Acta Arithmetica},
keywords = {zero density estimate; mean value; Selberg method; zeros of Hecke - functions; holomorphic cusp forms; Hafner's method},
language = {eng},
number = {2},
pages = {139-158},
title = {Zeros of Hecke L-functions associated with cusp forms},
url = {http://eudml.org/doc/206764},
volume = {71},
year = {1995},
}

TY - JOUR
AU - Wenzhi Luo
TI - Zeros of Hecke L-functions associated with cusp forms
JO - Acta Arithmetica
PY - 1995
VL - 71
IS - 2
SP - 139
EP - 158
LA - eng
KW - zero density estimate; mean value; Selberg method; zeros of Hecke - functions; holomorphic cusp forms; Hafner's method
UR - http://eudml.org/doc/206764
ER -

References

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  1. [1] E. Bombieri and D. A. Hejhal, On the distribution of zeros of linear combinations of Euler products, preprint, 1993. 
  2. [2] P. Deligne, Formes modulaires et représentations l-adiques, Sém. Bourbaki, 1968/69, exposés 355. 
  3. [3] P. Deligne, La conjecture de Weil, I, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 273-307. 
  4. [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. Zbl0671.10021
  5. [5] W. Duke, J. Friedlander and H. Iwaniec, Bound for automorphic L-functions, Invent. Math. 112 (1993), 1-8. Zbl0765.11038
  6. [6] D. Farmer, Mean value of Dirichlet series associated with holomorphic cusp forms, J. Number Theory, to appear. 
  7. [7] A. Good, Approximative Funktionalgleichungen und Mittelwertsätze für Dirichletreihen, die Spitzenformen assoziiert sind, Comment. Math. Helv. 50 (1975), 327-361. Zbl0315.10038
  8. [8] A. Good, Beiträge zur Theorie der Dirichletreihen, die Spitzenformen zugeordnet sind, J. Number Theory 13 (1981), 18-65. Zbl0446.10022
  9. [9] G. H. Hardy, Note on Ramanujan's function τ(n), Proc. Cambridge Philos. Soc. 23 (1927), 675-680. Zbl53.0150.01
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  12. [12] J. L. Hafner, Explicit estimates in the arithmetic theory of cusp forms and Poincaré series, Math. Ann. 264 (1983), 9-20. Zbl0497.10017
  13. [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. [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. [15] C. G. Lekkerkerker, On the zeros of a class of Dirichlet series, Dissertation, Utrecht, 1955. Zbl1173.30301
  16. [16] H. L. Montgomery and R. C. Vaughan, Hilbert's inequality, J. London Math. Soc. 8 (1974), 73-82. Zbl0281.10021
  17. [17] C. J. Moreno, Explicit formulas in the theory of automorphic forms, in: Lecture Notes in Math. 626, Springer, 1977, 73-216. 
  18. [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. Zbl0021.39202
  19. [19] A. Selberg, On the zeros of Riemann's zeta-function, in: Collected Papers, Vol. I, Springer, 1989, 85-141. 
  20. [20] A. Selberg, Contributions to the theory of the Riemann zeta-function, in: Collected Papers, Vol. I, Springer, 1989, 214-280. 
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  22. [22] E. C. Titchmarsh, The Theory of Functions, Oxford, 1952 Zbl0049.18603

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