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Asymptotic Expansions of Some Series Involving the Riemann Zeta Function


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1 University of Colorado, Boulder, Colorado, United States
     

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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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  • Asymptotic Expansions of Some Series Involving the Riemann Zeta Function

Abstract Views: 222  |  PDF Views: 0

Authors

S. Chowla
University of Colorado, Boulder, Colorado, United States
D. Hawkins
University of Colorado, Boulder, Colorado, United States

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.