Generalisations of Ramanujan sums for Polynomial rings over finite fields

2019/09/27 by Julio Andrade, Andrade, J. C., J.R.P. Hanslope +1
Mathematics · #11N37 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Graph theory and applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1909.12747

openalex publication_date 2019/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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