The Bessel function over finite fields

Abstract

In this article we study an analogue of the classical Bessel function over finite fields. The definition of the this function is associated with the explicit form of matrix elements for the irreducible representation of the group of motions on a plane over finite fields. For the Bessel function, we present the addition theorem, multiplication theorem, Hanson theorem and some others.

Keywords:

• Bessel function
• Finite field
• Group of motions
• Theory of groups representations

Acknowledgements

This work was supported by the grant Russian Science Support Foundation.