Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9496455 | Journal of Number Theory | 2005 | 35 Pages |
Abstract
Let E be an elliptic curve over F=Fq(t) having conductor (p)·â, where (p) is a prime ideal in Fq[t]. Let dâFq[t] be an irreducible polynomial of odd degree, and let K=F(d). Assume (p) remains prime in K. We prove the analogue of the formula of Gross for the special value L(EâFK,1). As a consequence, we obtain a formula for the order of the Tate-Shafarevich group Ш(E/K) when L(EâFK,1)â 0.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Mihran Papikian,