The series that Ramanujan misunderstood
Geoffrey B Campbell, Aleksander Zujev
TL;DR
This paper reevaluates a well-known oscillating power series linked to Ramanujan's incorrect prime distribution theory, offering new insights into its properties and historical context.
Contribution
It provides a novel analysis of Ramanujan's series, clarifying misconceptions and shedding light on its mathematical significance and historical interpretation.
Findings
Reinterprets Ramanujan's series in modern mathematical context
Clarifies misconceptions about Ramanujan's prime distribution theory
Offers new insights into the oscillatory behavior of the series
Abstract
We give a new appraisal of a famous oscillating power series considered by Hardy and Ramanujan related to the erroneous theory of distribution of primes by Ramanujan.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Mathematical functions and polynomials