p-adic Fourier transforms

Fourier transforms and p - adic Weil

Building on work of Crew, we give a rigid cohomological analogue of the main result of Deligne’s “Weil II”; this makes it possible to give a purely p-adic proof of the Weil conjectures. Ingredients include a p-adic analogue of Laumon’s application of the geometric Fourier transform in the l-adic setting, as well as recent results on p-adic differential equations, due to André, Christol, Crew, M...

p-Adic Fourier Theory

In this paper we generalize work of Amice and Lazard from the early sixties. Amice determined the dual of the space of locally Qp-analytic functions on Zp and showed that it is isomorphic to the ring of rigid functions on the open unit disk over Cp. Lazard showed that this ring has a divisor theory and that the classes of closed, finitely generated, and principal ideals in this ring coincide. W...

1 p - adic Fourier theory

In the early sixties, Amice ([Am1], [Am2]) studied the space of K-valued, locally analytic functions on Z Z p and formulated a complete description of its dual, the ring of K-valued, locally Q p-analytic distributions on Z Z p , when K is a complete subfield of C p. She found an isomorphism between the ring of distributions and the space of global functions on a rigid variety over K parameteriz...

Mellin transforms of p-adic Whittaker functions

BOUNDS FOR FOURIER TRANSFORMS OF REGULAR ORBITAL INTEGRALS ON p-ADIC LIE ALGEBRAS

Let G be a connected reductive p-adic group and let g be its Lie algebra. LetO be a G-orbit in g. Then the orbital integral μO corresponding to O is an invariant distribution on g, and Harish-Chandra proved that its Fourier transform μ̂O is a locally constant function on the set g′ of regular semisimple elements of g. Furthermore, he showed that a normalized version of the Fourier transform is l...