Explicit upper bound for the (analytic) rank of J0(q)

Israel Journal of Mathematics

Volumn 120, Issue , 2000, Pages 179-204

  Kowalski, E ^a   Michel, P ^b  

^a PRINCETON UNIVERSITY   (United States)

^b UNIV MONTPELLIER   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041081241     PISSN: 00212172     EISSN: 15658511     Source Type: Journal    
DOI: 10.1007/s11856-000-1276-8     Document Type: Article

References (11)

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3. W. Duke, The critical order of vanishing of automorphic L-functions with high level, Inventiones Mathematicae 119 (1995), 165-174.
4. H. Iwaniec and P. Sarnak, The non-vanishing of central values of automorphic L-functions and Siegel-Landau zeros, in preparation.
5. 0(q) and zeros of automorphic L-functions, Duke Mathematical Journal, to appear.
6. 0(q), Acta Arithmetica, to appear.
7. E. Kowalski, The rank of the Jacobian of modular curves: analytic methods, Ph.D. Thesis, Rutgers University, 1998.
8. B. Mazur and P. Swinnerton-Dyer, Arithmetic of Weil curves, Inventiones Mathematicae 25 (1974), 1-61.
9. A. Selberg, Contributions to the theory of Dirichlet's L-functions, Skrifter utgitt au Det Norske Videnskaps-Akademi i Oslo I. Mat.-Naturv. Klasse (1946), No. 3, 1-62, or Collected Papers, Vol. 1, Springer-Verlag, Berlin, 1989, pp. 281-340.
10. A. Selberg, Contributions to the theory of Dirichlet's L-functions, Skrifter utgitt au Det Norske Videnskaps-Akademi i Oslo I. Mat.-Naturv. Klasse (1946), No. 3, 1-62, or Collected Papers, Vol. 1, Springer-Verlag, Berlin, 1989, pp. 281-340.
11. E. C. Titchmarsh, The Theory of the Riemann Zeta Function, 2nd edition (revised by D. R. Heath-Brown), Oxford University Press, 1986.