Fourier transform over finite field and identities between Gauss sums

0 Fourier Transform over Finite Field and Identities between Gauss Sums

Pure Gauss Sums over Finite Fields

New classes of pairs e,p are presented for which the Gauss sums corresponding to characters of order e over finite fields of characteristic p are pure, i.e., have a real power. Certain pure Gauss sums are explicitly evaluated. §

The (finite field) Fast Fourier Transform

There are numerous directions from which one can approach the subject of the fast Fourier Transform (FFT). It can be explained via numerous connections to convolution, signal processing, and various other properties and applications of the algorithm. We (along with Geddes/Czapor/Labahn) take a rather simple view from the algebraic manipulation standpoint. As will be apparent shortly, we relate ...

The (finite field) Fast Fourier Transform

There are numerous directions from which one can approach the subject of the fast Fourier Transform (FFT). It can be explained via numerous connections to convolution, signal processing, and various other properties and applications of the algorithm. We (along with Geddes/Czapor/Labahn) take a rather simple view from the algebraic manipulation standpoint. As will be apparent shortly, we relate ...

The Fourier Transform and Equations over Finite Abelian Groups