Page 1 Next

Displaying 1 – 20 of 48

Showing per page

Chebyshev polynomials and Pell equations over finite fields

Boaz Cohen (2021)

Czechoslovak Mathematical Journal

We shall describe how to construct a fundamental solution for the Pell equation x 2 - m y 2 = 1 over finite fields of characteristic p 2 . Especially, a complete description of the structure of these fundamental solutions will be given using Chebyshev polynomials. Furthermore, we shall describe the structure of the solutions of the general Pell equation x 2 - m y 2 = n .

Generalized Kummer theory and its applications

Toru Komatsu (2009)

Annales mathématiques Blaise Pascal

In this report we study the arithmetic of Rikuna’s generic polynomial for the cyclic group of order n and obtain a generalized Kummer theory. It is useful under the condition that ζ k and ω k where ζ is a primitive n -th root of unity and ω = ζ + ζ - 1 . In particular, this result with ζ k implies the classical Kummer theory. We also present a method for calculating not only the conductor but also the Artin symbols of the cyclic extension which is defined by the Rikuna polynomial.

Currently displaying 1 – 20 of 48

Page 1 Next