Given a quaternionic form $$\textrm{G}$$ of p-adic classical group (p odd) we classify all cuspidal irreducible representations with coefficients in an algebraically closed field characteristic different from p. We prove two theorems: At first: Every representation is induced type, i.e. certain compact open subgroup , constructed $$\beta $$ -extension and finite group. Secondly show that intert...

The principal ideas of harmonic analysis on a locally compact group G which is not necessarily compact or commutative were developed in the 1940s and early 1950s. In this theory, the role of the classical fundamental harmonics is played by the irreducible unitary representations of G. The set of all equivalence classes of such representations is denoted by Ĝ and is called the dual object of G o...

In this paper, we construct explicit eigenfunctions of the local Weil representation on unitary group of one variable in the p-adic case where p is odd. The idea is to use the lattice model, and the results will be used to compute special values of certain Hecke L-functions in separated papers. We also recover Moen’s results on when a local theta lifting from U(1) to itself does not vanish. 0. ...

This article is the first in a series devoted to Kato’s Euler system arising from p-adic families of Beilinson elements in the K-theory of modular curves. It proves a p-adic Beilinson formula relating the syntomic regulator (in the sense of Coleman–de Shalit and Besser) of certain distinguished elements in the K-theory of modular curves to the special values at integer points ≥ 2 of the Mazur–S...