Exponential decay in the frequency of analytic ranks of automorphic L-functions
D. R. Heath-Brown and P. Michel
Source: Duke Math. J. Volume 102, Number 3 (2000), 475-484.
First Page PDF: View first page of article (PDF, 30 KB)Primary Subjects: 11F66
Secondary Subjects: 11F30, 11G40, 11M36
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1092749339
Mathematical Reviews number (MathSciNet):
MR1756106
Digital Object Identifier: doi:10.1215/S0012-7094-00-10235-9
Zentralblatt MATH identifier:
01455498
References
É. Fouvry, ``Sur le comportement en moyenne du rang des courbes $y\sp 2=x\sp 3+k$'' in Séminaire de Théorie des Nombres (Paris, 1990--91.), Progr. Math. 108, Birkhäuser, Boston, 1993, 61--84.
Mathematical Reviews (MathSciNet):
MR1263524
D. R. Heath-Brown, The size of Selmer groups for the congruent number problem, Invent. Math. 111 (1993), 171--195.
Mathematical Reviews (MathSciNet):
MR1193603
Digital Object Identifier: doi:10.1007/BF01231285
--. --. --. --., The size of Selmer groups for the congruent number problem, II, Invent. Math. 118 (1994), 331--370.
Mathematical Reviews (MathSciNet):
MR1292115
Digital Object Identifier: doi:10.1007/BF01231536
E. Kowalski and P. Michel, The analytic rank of $J_0(q)$ and zeros of automorphic $L$-functions, Duke Math. J. 100 (1999), 503--542.
Mathematical Reviews (MathSciNet):
MR1719730
Digital Object Identifier: doi:10.1215/S0012-7094-99-10017-2
Project Euclid: euclid.dmj/1077227496
--------, An explicit upper bound for the rank of $J_0(q)$, to appear in Israel J. Math.
E. Kowalski, P. Michel, and J. M. VanderKam, Non-vanishing of high derivatives of automorphic $L$-functions at the center of the critical strip, to appear in J. Reine Angew. Math.
Mathematical Reviews (MathSciNet):
MR1778299
M. Ram Murty, ``The analytic rank of $J_0(N)$($\mathbbQ$)'' in Number Theory (Halifax, N.S., 1994), CMS Conf. Proc. 15, Amer. Math. Soc., Providence, 1995, 263--277.
Mathematical Reviews (MathSciNet):
MR1353938
A. Selberg, Contributions to the theory of Dirichlet's $L$-functions, Skr. Norske Vid.-Akad. Oslo I Mat.-Nat. Kl. 1946, no. 3.
Duke Mathematical Journal
