Ramanujan expansions of arithmetic functions of several variables over \mathbbF_q[T]

2018/11/05 by Tianfang Qi, Qi, Tianfang, Su Hu +1
Computer Science · Mathematics · #11L05 (Secondary) #11T24 (Primary) #11T55 #Advanced Mathematical Identities #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11L05 #msc:11T24 #msc:11T55

paper · pdf · doi:10.48550/arxiv.1811.01654

27 pages

openalex publication_date 2018/11/05 · arxiv created 2019/09/29 · arxiv updated 2019/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathbbA=\mathbbF_q[T] be the polynomial ring over finite field \mathbbF_q, and \mathbbA₊ be the set of monic polynomials in \mathbbA. In this paper, we show that a large class of arithmetic functions in multi-variables over \mathbbA₊ can be expanded through the polynomial Ramanujan sums and the unitary polynomial Ramanujan sums. These are analogues of classical results over ℕ by Winter, Delange and Tóth.

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