Generalisations of Ramanujan sums for Polynomial rings over finite fields

J. C. Andrade; J. R. P. Hanslope

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arXiv · 1909.12747

Generalisations of Ramanujan sums for Polynomial rings over finite fields

J. C. Andrade·J. R. P. Hanslope

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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.

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BibTeX RIS

J. C. Andrade, J. R. P. Hanslope. 2019-09-27. Generalisations of Ramanujan sums for Polynomial rings over finite fields. https://arxiv.org/abs/1909.12747

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