Some Tauberian Theorems Connected with the Prime Number Theorem

Citation

Gordon, Basil (1956) Some Tauberian Theorems Connected with the Prime Number Theorem. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/952N-ET02. https://resolver.caltech.edu/CaltechETD:etd-03232004-113001

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. 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) = [...](x).

Item Type:	Thesis (Dissertation (Ph.D.))
Subject Keywords:	(Mathematics and Physics)
Degree Grantor:	California Institute of Technology
Division:	Physics, Mathematics and Astronomy
Major Option:	Mathematics
Minor Option:	Physics
Thesis Availability:	Public (worldwide access)
Research Advisor(s):	Apostol, Tom M.
Thesis Committee:	Unknown, Unknown
Defense Date:	1 January 1956
Record Number:	CaltechETD:etd-03232004-113001
Persistent URL:	https://resolver.caltech.edu/CaltechETD:etd-03232004-113001
DOI:	10.7907/952N-ET02
Default Usage Policy:	No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:	1063
Collection:	CaltechTHESIS
Deposited By:	Imported from ETD-db
Deposited On:	23 Mar 2004
Last Modified:	13 Jul 2023 17:58

Thesis Files

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