English

Generalisations of Ramanujan sums for Polynomial rings over finite fields

Number Theory 2019-09-30 v1

Abstract

In this paper, we consider a general form of the analogue of Ramanujan's sum in the ring of polynomials over a finite field. We first prove some multiplicative properties of such functions before considering their finite Fourier series and some specific examples. In the end, we also prove a result about the Dirichlet series of such functions.

Keywords

Cite

@article{arxiv.1909.12747,
  title  = {Generalisations of Ramanujan sums for Polynomial rings over finite fields},
  author = {J. C. Andrade and J. R. P. Hanslope},
  journal= {arXiv preprint arXiv:1909.12747},
  year   = {2019}
}

Comments

13 pages; comments are welcome