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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. http://resolver.caltech.edu/CaltechETD:etd-03232004-113001

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) = [...](x).

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
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:http://resolver.caltech.edu/CaltechETD:etd-03232004-113001
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:26 Dec 2012 02:34

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