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Elliptic curves with CM by and 3-adic valuations of their L-series

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Abstract

 Consider elliptic curves defined over the quadratic field ℚ. Hecke L-series attached to E are studied, formulae for their values at , and bound of 3-adic valuations of these values are given. These results are consistent with the predictions of the conjecture of Birch and Swinnerton-Dyer, and develop some results in recent literature.

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Authors and Affiliations

  1. Tsinghua University, Center for Advanced Study, Beijing 100084, China, , , , , , CN

    Qiu Derong

  2. Tsinghua University, Department of Mathematics, Beijing 100084, China. e-mail: xianke@tsinghua.edu.cn, , , , , , CN

    Zhang Xianke

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  1. Qiu Derong
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  2. Zhang Xianke
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Received: 28 February 2001 / Revised version: 14 December 2001

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Derong, Q., Xianke, Z. Elliptic curves with CM by and 3-adic valuations of their L-series. Manuscripta Math. 108, 385–397 (2002). https://doi.org/10.1007/s002290200270

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  • DOI: https://doi.org/10.1007/s002290200270

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