A Tauberian Theorem and Analogues of the Prime Number Theorem Journal Articles uri icon

  •  
  • Overview
  •  
  • Research
  •  
  • Identity
  •  
  • Additional Document Info
  •  
  • View All
  •  

abstract

  • In 1945 Ingham (3) proved the following Tauberian theorem: if ƒ is a non-decreasing, non-negative function on [1, ∞) and1then 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).

publication date

  • 1968