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A Tauberian Theorem and Analogues of the Prime Number Theorem
Published online by Cambridge University Press: 20 November 2018
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In 1945 Ingham (3) proved the following Tauberian theorem: if ƒ is a non-decreasing, non-negative function on [1, ∞) and
1
then ƒ(x) ∼ cx. His proof is based on the non-vanishing of the Riemann zeta-function, ζ (s), on the line , and uses Pitt's form of Wiener's Tauberian theorem; (see, e.g., 5, Theorem 109, p. 211).
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- Copyright © Canadian Mathematical Society 1968
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