We study a problem concerning parabolic induction in certain p-adic unitary groups. More precisely, for $E/F$ quadratic extension of fields the associated group $G=\mathrm{U}(n,n)$ contains subgroup $P$ with Levi component $L$ isomorphic to $\mathrm{GL}_n(E)$. Let $\pi$ be an irreducible supercuspidal representation depth zero. use Hecke algebra methods determine when parabolically induced $\io...

We determine the admissible nilpotent coadjoint orbits of real and p-adic split exceptional groups of types G2, F4, E6 and E7. We find that all Lusztig-Spaltenstein special orbits are admissible. Moreover, there exist nonspecial admissible orbits, corresponding to “completely odd” orbits in Lusztig’s special pieces. In addition, we determine the number of, and representatives for, the non-even ...

We are interested in understanding and describing the p-adic properties of Jacobi forms. As opposed to the case of modular forms, not much work has been done in this area. The literature includes [3, 4, 7]. In the first section, we follow Serre’s ideas from his theory of p-adic modular forms. We study Jacobi forms whose Fourier expansions have integral coefficients and look at congruences betwe...

The theory of p-adic modular forms was developed by J.-P. Serre [8] and N. Katz [5]. This theory is by now considered classical. Investigation of p-adic congruences for modular forms of half-integer weight was carried out by N. Koblitz [6] and led him to deep conjectures. It seems natural to search for p-adic properties of other types of automorphic forms. In this paper we use the Serre approac...

Ming-Lun Hsieh constructed three-variable triple product p-adic L-functions attached to triples of primitive Hida families and proved interpolation formulas. We generalize his result in the unbalanced case construct a L-function family two more general modular forms.