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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. https://resolver.caltech.edu/CaltechAUTHORS:20221028-653838600.6

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Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s41745-022-00313-0DOIArticle
ORCID:
AuthorORCID
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.
Funders:
Funding AgencyGrant Number
NSFDMS-2001409
Issue or Number:3
DOI:10.1007/s41745-022-00313-0
Record Number:CaltechAUTHORS:20221028-653838600.6
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20221028-653838600.6
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:117641
Collection:CaltechAUTHORS
Deposited By: Research Services Depository
Deposited On:08 Nov 2022 19:43
Last Modified:25 Jan 2023 20:30

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