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A Generalisation of Ramanujan's (back of the envelope) Method for Divergent Series

2023/03/24 by Burchell, Patrick J.
#05A15 (Secondary) #11C08 (Primary) #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2303.14045

Abstract

Ramanujan derived the well known divergent-sum of integers in more than one way. We generalise the informal method to higher powers of the Riemann zeta function through a study of the Eulerian numbers in particular. Within the context of additive combinatorics a heuristic approach that unifies generating series and difference matrices is presented.

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