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On the weak forms of the 2-part of Birch and Swinnerton-Dyer conjecture

Published online by Cambridge University Press:  05 September 2018

SHUAI ZHAI
SHUAI ZHAI*
Affiliation:
Institute for Advanced Research, Shandong University, Jinan, Shandong 250100, China. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road. Cambridge CB3 0WBU.K. e-mail: shuaizhai@gmail.com
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Abstract

In this paper, we investigate the weak forms of the 2-part of the conjecture of Birch and Swinnerton-Dyer, and prove a lower bound for the 2-adic valuation of the algebraic part of the central value of the complex L-series for the family of quadratic twists of all optimal elliptic curves over ${\mathbb Q}$.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 1 , January 2020 , pp. 197 - 209
Copyright
Copyright © Cambridge Philosophical Society 2018 

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Footnotes

†

Supported by Shandong Province Natural Science Foundation (Grant No. ZR2016AP03)

References

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