AUTOMORPHY FOR SOME l-ADIC LIFTS OF AUTOMORPHIC

Automorphy for some l-adic lifts of automorphic modl Galois representations. II

On Symmetric Power L-invariants of Iwahori Level Hilbert Modular Forms

We compute the arithmetic L-invariants (of Greenberg–Benois) of twists of symmetric powers of p-adic Galois representations attached to Iwahori level Hilbert modular forms (under some technical conditions). Our method uses the automorphy of symmetric powers and the study of analytic Galois representations on p-adic families of automorphic forms over symplectic and unitary groups. Combining thes...

Evolution Equations in Generalized Stepanov-like Pseudo Almost Automorphic Spaces

In this article, first we introduce and study the concept of Sγ pseudo almost automorphy (or generalized Stepanov-like pseudo almost automorphy), which is more general than the notion of Stepanov-like pseudo almost automorphy due to Diagana. We next study the existence of solutions to some classes of nonautonomous differential equations of Sobolev type in Sγ -pseudo almost automorphic spaces. T...

Some bounds on unitary duals of classical groups‎ - ‎non-archimeden case

‎We first give bounds for domains where the unitarizabile subquotients can show up in the parabolically induced representations of classical $p$-adic groups‎. ‎Roughly‎, ‎they can show up only if the‎ ‎central character of the inducing irreducible cuspidal representation is dominated by the‎ ‎square root of the modular character of the minimal parabolic subgroup‎. ‎For unitarizable subquotients...

Slopes of Modular Forms

Motivation: it would be great if we could understand the p-adic variation of the Up-eigenvalues of modular forms as the weights and/or levels varied. (More generally, it would be really great if we could understand how the local p-adic Galois representations attached to automorphic forms behave – for example, even very weak “equidistribution” results here would presumably imply very strong auto...