×

zbMATH — the first resource for mathematics

The \(p\)-adic finite Fourier transform and theta functions. (English) Zbl 0929.14027
Let \(H\) be a finite group. \(\widehat H=\operatorname{Hom}(H,k^*)\) its group of characters over a field \(k\) and \(V(H)\) the vector space of \(k\)-valued functions on \(H\). The finite Fourier transform is a linear isomorphism \(F_A:V(H)\to V(\widehat H)\) which is explicitly computed. The author also states the explicit actions of the Heisenberg group \({\mathcal G}(H\times\widehat H)\) on \(V(H)\) and \(V(\widehat H)\).
The last section is devoted to applications to the study of theta functions on an analytic torus.
MSC:
14K25 Theta functions and abelian varieties
14G20 Local ground fields in algebraic geometry
14C20 Divisors, linear systems, invertible sheaves
PDF BibTeX XML Cite
Full Text: EuDML