ICTP Mathematics Seminar - Friday 24 April at 16:30

[Margherita Di Giovannantonio]

M A T H E M A T I C S   S E M I N A R S   2015

Friday, 24 April, at 16:30 hrs.


Carlos Castano-Bernard (Universidad de Colima, Mexico)

Title: On a refinement of a conjecture of Gross-Kohnen-Zagier


Summary:
Let E be an elliptic curve over the field of rational numbers and let 
L(E, s) be its L-function. The Birch and Swinnerton-Dyer formula 
predicts that the first non-zero coefficient of the Taylor expansion of 
L(E, s) around s = 1 encodes some important arithmetic invariants 
attached to E. Assume that L(E, s) has a simple zero at s = 1. By the 
work of Wei Zhang we know that the p-part of the BSD formula holds for 
all primes p greater or equal to 5. Recently, Chao Li has obtained some 
interesting results for p = 2. In this talk we shall discuss a 
refinement of the 2-part of the conjecture introduced in the 
Gross-Kohnen-Zagier (1987) paper that seems resonant with some aspects 
of Chao Li's recent results. The talk is intended for a non-specialist 
audience and we will focus mostly on some explicit examples.



Venue:  Luigi Stasi Seminar Room (ICTP Leonardo da Vinci Building, first 
floor)