Some Tauberian Theorems Connected with the Prime Number Theorem

Author: Gordon, Basil

Year: 1956

Degree: Dissertation (Ph.D.)

Advisor: Apostol, Tom M.

Committee Member: Unknown, Unknown

Option: Mathematics; Physics

DOI: 10.7907/952N-ET02

Abstract

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Let A(x) be a monotone non-decreasing function of x, and let [...]. It is possible that T(x)~ ax log x, but [...] = 0, [...]. If T(x) = ax log x + 0(x), then [...], [...], but A(x) ~ ax is in general false. If T(x) = ax log x + bx + [...] then A(x) ~ ax.

The prime number theorem is the special case A(x) = ....

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