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A p-adic Waldspurger Formula and the Conjecture of Birch and Swinnerton-Dyer

Burungale, Ashay A. (2022) A p-adic Waldspurger Formula and the Conjecture of Birch and Swinnerton-Dyer. Journal of the Indian Institute of Science, 102 (3). pp. 885-894. ISSN 0970-4140. doi:10.1007/s41745-022-00313-0.

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About a decade ago Bertolini–Darmon–Prasanna proved a p-adic Waldspurger formula, which expresses values of an anticyclotomic p-adic L-function associated to an elliptic curve E/ℚ outside its defining range of interpolation in terms of the p-adic logarithm of Heegner points on E. In the ensuing decade an insight of Skinner based on the p-adic Waldspurger formula has initiated a progress towards the Birch and Swinnerton-Dyer conjecture for elliptic curves over ℚ, especially rank one aspects. In this note we outline some of this recent progress.

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Burungale, Ashay A.0000-0002-2469-2115
Additional Information:The note owes its existence to a suggestion of Mahesh Kakde, to whom the author is grateful for this opportunity as well as continual encouragement. The author would like to express his sincere gratitude to Chris Skinner and Ye Tian for generous and inspiring discussions. We thank the referee for helpful comments. The work was partially supported by the National Science Foundation Grant DMS-2001409.
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Issue or Number:3
Record Number:CaltechAUTHORS:20221028-653838600.6
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ID Code:117641
Deposited By: Research Services Depository
Deposited On:08 Nov 2022 19:43
Last Modified:25 Jan 2023 20:30

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