ICTP Mathematics Seminar - Wednesday 28 October at 14:30

[Margherita Di Giovannantonio]

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

Wednesday, 28 October, at 14:30 hrs.



Baskar Balasubramanyam (IISER Pune)



Special values of L-functions and congruences of modular forms


Abstract:
Let f and g be two modular forms that are eigenvectors for all the Hecke 
operators. Let \lambda_f (n) and \lambda_g (n) be the respective 
eigenvalues for the T(n) operator. Then f and g are said to be congruent 
mod a prime p if \lambda_f (n) is congruent to \lambda_g (n) mod p, for 
all n. Such congruences have been historically important have lead to 
studying p-adic families of modular forms. In the early 80s, Hida proved 
an important relationship between congruences and the special values of 
certain L-functions attached to modular forms. In my talk, I will review 
these results and discuss some of its generalizations.




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