Ramanujan Sums as Derivatives

2016/11/10 by Devendra Kumar Yadav, Yadav, Devendra Kumar, Gajraj Kuldeep +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #FOS: Mathematics #Fractal and DNA sequence analysis #General Mathematics (math.GM) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1611.04462

openalex publication_date 2016/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1918 S. Ramanujan defined a family of trigonometric sum now known as Ramanujan sums. In the last few years, Ramanujan sums have inspired the signal processing community. In this paper, we have defined an operator termed here as Ramanujan operator. In this paper it has been proved that these operator possesses properties of first derivative and second derivative with a particular shift. Generalised multiplicative property and new method of computing Ramanujan sums are also derived in terms of interpolation.

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