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The even parity Goldfeld conjecture: Congruent number elliptic curves

Burungale, Ashay and Tian, Ye (2022) The even parity Goldfeld conjecture: Congruent number elliptic curves. Journal of Number Theory, 230 . pp. 161-195. ISSN 0022-314X. doi:10.1016/j.jnt.2021.05.001.

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In 1979 Goldfeld conjectured: 50% of the quadratic twists of an elliptic curve defined over the rationals have analytic rank zero. In this expository article we present a few recent developments towards the conjecture, especially its first instance - the congruent number elliptic curves.

Item Type:Article
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URLURL TypeDescription Paper
Burungale, Ashay0000-0002-2469-2115
Additional Information:© 2021 Elsevier Inc. Received 13 April 2021, Accepted 31 May 2021, Available online 29 June 2021. It is a pleasure to thank John Coates, Wei He, Shinichi Kobayashi, Jinzhao Pan, Dinakar Ramakrishnan, Alex Smith, Richard Taylor and Wei Zhang for helpful discussions and instructive comments. The authors cordially thank Chris Skinner and Shou-Wu Zhang for inspiring conversations. The article owes its existence to a generous suggestion of Dorian Goldfeld. The authors would like to express their sincere gratitude to Dorian Goldfeld also for his enticing conjecture. A.B. is partially supported by the NSF grant DMS #2001409, and Y.T. by the NSFC grants #11688101 and #11531008.
Funding AgencyGrant Number
National Natural Science Foundation of China11688101
National Natural Science Foundation of China11531008
Subject Keywords:L-function; Selmer group; Goldfeld conjecture; BSD conjecture; Quadratic twist; Tunnell's theorem; Congruent numbers
Record Number:CaltechAUTHORS:20210714-164422990
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Official Citation:Ashay Burungale, Ye Tian, The even parity Goldfeld conjecture: Congruent number elliptic curves, Journal of Number Theory, Volume 230, 2022, Pages 161-195, ISSN 0022-314X,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109813
Deposited By: Tony Diaz
Deposited On:14 Jul 2021 17:22
Last Modified:26 Oct 2021 16:00

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