Mathematics

Dr. Matteo Longo
Department of Mathematics,Universities of Padua

Given a modular form f of even weight k and a quadratic imaginary field K, one can form a p-adic L-function L_p interpolating central critical values of the complex L-function of f twisted by characters of the anticyclotomic Z_p-extension of K. Under suitable parity conditions, one shows that this p-adic L-function is non-zero, and we can consider its \\lambda and \\mu Iwasawa invariants. When f lives in a Hida family, we show that these invariants are constants on branches, obtaining an anticyclotomic analogue of a similar result by Emerton-Pollack-Weston in the cyclotomic setting. This result allows us to spread results on the main conjecture from one form to all other forms in the family, obtaining new cases of the anticyclotomic main conjecture. This is a joint work with F. Castella and C.-H. Kim.