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Showing 1 to 2 of 2 for “"Birch-Swinnerton-Dyer conjecture"”.
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On the main conjectures of Iwasawa theory for certain elliptic curves with complex multiplication
The conjecture of Birch and Swinnerton-Dyer is unquestionably one of the most important open problems in number theory today. Let $E$ be an elliptic curve defined over an imaginary quadratic field $K$ contained in $\mathbb{C}$, and suppose that $E$ has complex multiplication by the ring of integers …
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Character Theory and Artin L-functions
… ranks of elliptic curves as predicted by the Birch-Swinnerton-Dyer conjecture. In a different vein, we employ the theory of supercharacters introduced by Diaconis and Isaacs to derive a supercharacter-theoretic analogue of Heilbronn characters. Moreover, we generalise the effective Chebotarev …