Karoubi theory of finite fields

Theory of wavelet transform over finite fields

In this paper, we develop the theory of the wavelet transform over Galois elds. To avoid the limitations inherent in the number theoretic Fourier transform over nite elds, our wavelet transform relies on a basis decomposition in the time domain rather than in the frequency domain. First, we characterize the in nite dimensional vector spaces for which an orthonormal basis expansion of any sequen...

Contributions to the Theory of Finite Fields*

The present paper contains a number of results in the theory of finite fields or higher congruences. The method may be considered as an appUcation of the theory of /»-polynomials, which I have developed in a recent paperf On a special class of polynomials. In this special case the /»-polynomials form a commutative ring. However, this paper may be read without reference to the former investigati...

Algebraic K-theory of Finite Fields

On the K-theory of Finite Fields

In this talk we introduce higher algebraicK-groups via Quillen’s plus construction.We then give a brief tour of algebraicK-theory and its relation to stable homotopy theory and number theory — in particular noting that aK-theory computation of the integers is equivalent to the Kummer–Vandiver conjecture. We next state Quillen’s computations of the K-theory of Fq and Fq. The remainder of the tal...

The Elementary Theory of Finite Fields