Wach Modules and Iwasawa Theory for Modular Forms

Iwasawa theory of overconvergent modular forms, I: Critical-slope p-adic L-functions

We construct an Euler system of p-adic zeta elements over the eigencurve which interpolates Kato’s zeta elements over all classical points. Applying a big regulator map gives rise to a purely algebraic construction of a two-variable p-adic L-function over the eigencurve. As a first application of these ideas, we prove the equality of the p-adic L-functions associated with a critical-slope refin...

Galois modules, Iwasawa theory and leading term conjectures

Eichler-shimura Theory for Mock Modular Forms

We use mock modular forms to compute generating functions for the critical values of modular L-functions, and we answer a generalized form of a question of Kohnen and Zagier by deriving the “extra relation” that is satisfied by even periods of weakly holomorphic cusp forms. To obtain these results we derive an Eichler-Shimura theory for weakly holomorphic modular forms and mock modular forms. T...

Analytic Theory of Modular Forms

Filtrations of smooth principal series and Iwasawa modules

Let $G$ be a reductive $p$-adic group‎. ‎We consider the general question‎ ‎of whether the reducibility of an induced representation can be detected in a‎ ‎``co-rank one‎" ‎situation‎. ‎For smooth complex representations induced from supercuspidal‎ ‎representations‎, ‎we show that a sufficient condition is the existence of a subquotient‎ ‎that does not appear as a subrepresentation‎. ‎An import...