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On p-adic valuations of L(1) of elliptic curves with CM by √-3

Published online by Cambridge University Press:  12 July 2007

Derong Qiu
Derong Qiu
Affiliation:
Center for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China ([email protected])
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Abstract

For positive rational integers λ, we study the Hecke L-series attached to elliptic curves y2 = x3 − 2433Dλ over the quadratic field Q(√−3) and obtain various bounds of p(= 2, 3)-adic valuations of their values at s = 1 according to the cases of D and λ. In particular, for the case of even λ, we obtain a criterion of reaching the bounds of 3-adic valuations. From this, combining with the work of Coates and Wiles and Rubin, we obtain some results about the conjecture of Birch and Swinnerton-Dyer of these curves.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 133 , Issue 6 , December 2003 , pp. 1389 - 1407
Copyright
Copyright © Royal Society of Edinburgh 2003

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