Periods of Cusp Forms and Elliptic Curves over Imaginary Quadratic Fields
نویسنده
چکیده
In this paper we explore the arithmetic correspondence between, on the one hand, (isogeny classes of) elliptic curves E defined over an imaginary quadratic field K of class number one, and on the other hand, rational newforms F of weight two for the congruence subgroups r0(n), where n is an ideal in the ring of integers R of K . This continues work of the first author and forms part of the Ph.D. thesis of the second author. In each case we compute numerically the value of the L-series L(F, s) at s = 1 and compare with the value of L(E, 1 ) which is predicted by the Birch-Swinnerton-Dyer conjecture, finding agreement to several decimal places. In particular, we find that L(F, 1) = 0 whenever E(K) has a point of infinite order. Several examples are given in detail from the extensive tables computed by the authors.
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