Published September 15, 2022
| Version public
Journal Article
A p-adic Waldspurger Formula and the Conjecture of Birch and Swinnerton-Dyer
Creators
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1.
California Institute of Technology
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2.
The University of Texas at Austin
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.
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.Additional details
Identifiers
- Eprint ID
- 117641
- Resolver ID
- CaltechAUTHORS:20221028-653838600.6
Funding
- NSF
- DMS-2001409
Dates
- Created
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2022-11-08Created from EPrint's datestamp field
- Updated
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2023-01-25Created from EPrint's last_modified field