2012/12/12 by Geoffrey B. Campbell, Campbell, Geoffrey B.
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT) #math-ph #math.CO #math.MP #math.NT
paper · pdf · doi:10.48550/arxiv.1212.2818
24 pages, 1 figure. Incidental paper to monograph in progress
arxiv created 2012/12/12 · openalex publication_date 2012/12/12 · arxiv updated 2012/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define an extension of the Ramanujan trigonometric function to arbitrary dimensions, and give the Dirichlet series generating function. The extension was first given by Eckford Cohen long ago. This links directly to visible point vector identities, and possibly to lattice sums in Physics and Chemistry presented by Baake et al. New generating functions and summations are given here, generalizing the Ramanujan function, Euler totient and the Jordan totient functions, based on visible lattice point ideas.