Bulletin of Pure and Applied Sciences Section.
  • Year: 2019
  • Volume: 38E
  • Issue: 1

Computation of Jacobi Sums and Cyclotomic Numbers with Reduced Complexity

1Department of Mathematics, Central University of Jharkhand, Ranchi, Jharkhand835205, India

2Department of Mathematics, Central University of Jharkhand, Ranchi, Jharkhand835205, India

*Md. Helal Ahmed, Department of Mathematics, Central University of Jharkhand, Ranchi, Jharkhand 835205, India. E-mail: ahmed.helal@cuj.ac.in

**E-mail: jagmohan.t@gmail.com

Abstract

Jacobi sums and cyclotomic numbers are the important objects in number theory. The determination of all the Jacobi sums and cyclotomic numbers of order e is merely intricate to compute. This paper presents the lesser numbers of Jacobi sums and cyclotomic numbers which are enough for the determination all Jacobi sums and the cyclotomic numbers of a particular order.

Keywords

Character, Cyclotomic numbers, Jacobi sums, Finite fields, Cyclotomic polynomial, Primary, 11T24, Secondary, 11T22