On a theorem of Bertolini-Darmon on the rationality of Stark-Heegner points over genus fields of real quadratic fields
Author:
Chung Pang Mok
Journal:
Trans. Amer. Math. Soc. 374 (2021), 1391-1419
MSC (2020):
Primary 11G05, 11G40
DOI:
https://doi.org/10.1090/tran/8254
Published electronically:
November 25, 2020
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Abstract | References | Similar Articles | Additional Information
Abstract: In this paper, we remove certain hypotheses in the theorem of Bertolini-Darmon on the rationality of Stark-Heegner points over narrow genus class fields of real quadratic fields. Along the way, we establish that certain normalized special values of -functions are squares of rational numbers, a result that is of independent interest, and can be regarded as instances of the rank zero case of the Birch and Swinnerton-Dyer conjecture modulo squares.
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Additional Information
Chung Pang Mok
Affiliation:
School of Mathematical Sciences, Soochow University, 1 Shi-Zi Street, Suzhou 215006, Jiangsu Province, China
Email:
zpmo@suda.edu.cn
DOI:
https://doi.org/10.1090/tran/8254
Keywords:
Elliptic curves,
special values of $L$-functions.
Received by editor(s):
September 12, 2019
Received by editor(s) in revised form:
July 3, 2020
Published electronically:
November 25, 2020
Article copyright:
© Copyright 2020
American Mathematical Society