On exceptional zero conjecture Mazur-Tate-Teitelbaum by Srilakshmi Krishnamoorthy

12 December 2016 to 22 December 2016 VENUE : Madhava Lecture Hall ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory specifically in arithmetic geometry that has abundant numerical evidence but not a complete general solution.
An elliptic curve say E can be represented by points on a cubic equation as below with certain A B ? Q: y2 x3 Ax B A Theorem of Mordell says that that EQ the set of rational points of E is a finitely generated abelian group and thus EQ Zr ? T for some non-negative integer r and a finite group T.
Here r is called the algebraic rank of E. The Birch and Swinnerton-Dyer conjecture relates the algebraic rank of E to the value of the L-function LE s attached to E at s 1. Further theoretical understanding corroborated by computations lead to a stronger version of the BSD conjecture.
This refined version of the BSD conjecture provides a very precise formula for the leading term of LE s at s 1 the coefficient of s - 1r in terms of various arithmetical data attached to E.
Thus the computational side of the BSD conjecture goes hand in hand with the advanced concepts in the theory of Elliptic curves. In this program the computational aspects of the BSD conjecture with various illustrative examples as well as p-adic L-functions which are the p-adic analogues of the L-functions and other theoretical aspects which are important for the BSD conjecture will be discussed. CONTACT US: bsdtcicts.res.in PROGRAM LINK: Table of Contents powered by 0:00:00 Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture 0:00:04 Madhava lecture hall at the ICTS Campus Bangalore India 0:00:08 On exceptional zero conjecture Mazur-Tate-Teitelbaum 0:00:12 Recall - Interpolation property 0:02:12 Proof by Kobayashi - Recall 0:14:36 Coleman map 0:18:34 Definition of Coleman map 0:20:40 Dual map 0:21:06 Property of exp 0:33:06 To prove 0:37:29 Proof

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