Asymptotic Expansions of Some Series Involving the Riemann Zeta Function

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Authors

  • University of Colorado, Boulder, Colorado ,US
  • University of Colorado, Boulder, Colorado ,US

DOI:

https://doi.org/10.18311/jims/1962/16885

Abstract

HARDY and Littlewood (stimulated by a conjecture of Ramanujan) proved that the truth of

Σ (-l)nXn/n! Z(2n+1) = 0(X-i+∈)

(∈ > 0 arbitrary) is a necessary and sufficient condition for the truth of the Riemann hypothesis. Here Z(s) is Riemann's Zeta Function.

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Published

1962-09-01

How to Cite

Chowla, S., & Hawkins, D. (1962). Asymptotic Expansions of Some Series Involving the Riemann Zeta Function. The Journal of the Indian Mathematical Society, 26(3-4), 115–124. https://doi.org/10.18311/jims/1962/16885