The {$p$}-adic finite Fourier transform and theta functions
نویسندگان
چکیده
منابع مشابه
Abelian Varieties , Theta Functions and the Fourier Transform
This book is a modern introduction to the theory of abelian varieties and theta functions.Here the Fourier transform techniques play a central role, appearing in several different contexts. In transcendental theory, the usual Fourier transform plays a major role in the representation theory of the Heisenberg group, the main building block for the theory of theta functions. Also, the Fourier tra...
متن کاملp-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...
متن کاملThe Theta Multiplier via P - Adic Planes
Given any number eld and Dirichlet character for that eld, we construct a theta function on a restricted product of p-adic half-planes. An explicit formula for the theta multiplier is obtained through local calculations.
متن کاملFinite Fourier Transform, Circulant Matrices, and the Fast Fourier Transform
Suppose we have a function s(t) that measures the sound level at time t of an analog audio signal. We assume that s(t) is piecewise-continuous and of finite duration: s(t) = 0 when t is outside some interval a ≤ t ≤ b. Make a change of variable x = (t− a)/(b− a) and set f(x) = s(t). Then 0 ≤ x ≤ 1 when a ≤ t ≤ b, and f(x) is a piecewise continuous function of x. We convert f(x) into a digital s...
متن کامل1 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 1997
ISSN: 1370-1444
DOI: 10.36045/bbms/1105736873