A Caltech Library Service

Some Tauberian theorems connected with the prime number theorem


Gordon, Basil (1956) Some Tauberian theorems connected with the prime number theorem. Dissertation (Ph.D.), California Institute of Technology.


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.))
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:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1063
Deposited By: Imported from ETD-db
Deposited On:23 Mar 2004
Last Modified:26 Dec 2012 02:34

Thesis Files

PDF (Gordon_b_1956.pdf) - Final Version
See Usage Policy.


Repository Staff Only: item control page