Starts 28 Oct 2015 14:30
Ends 28 Oct 2015 16:00
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Special values of L-functions and congruences of modular forms
ICTP
Leonardo Building - Luigi Stasi Seminar Room
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.
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.