Number Theoretic Density
and
Logical Limit Laws

Stanley N. Burris
E-mail: snburris@math.uwaterloo.ca

Mathematical Surveys and Monographs Series
© American Mathematical Society
ISBN 0-8218-2666-2
Available from the AMS bookstore (www.ams.org)

Table of Contents [ PDF ] [ PS ]
Preface [ PDF ] [ PS ]
Overview [ PDF ] [ PS ]

Errata to Text


UPDATES
Some Outstanding Open Problems
  1. Find an example of a number system in RT_rho whose generating function diverges at rho with the property that some partition set does not have asymptotic density.
  2. Find an example of a number system in RV_alpha whose generating function diverges at alpha with the property that some partition set does not have asymptotic density.
  3. Give a multiplicative analog of the results of Woods.

My Related Preprint(s)

(1) (with Jason P. Bell)
Partition Identities I.
Sandwich Theorems and Logical 0--1 Laws
[ PS ] [ DVI ] [ PDF ]
(2) (with Jason P. Bell)
Partition Identities II.
The Results of Bateman and Erdos
[ PS ] [ DVI ] [ PDF ]
(3) (with Jason P. Bell)
Asymptotics for Logical Limit Laws.
When the Growth of the Components is in an RT Class.
Trans. Amer. Math. Soc. 355 (2003), 3777--3794.

[ PS ] [ DVI ] [ PDF ]
(4) (with Jason P. Bell )
Dirichlet Density Extends Global Asymptotic Density in Multiplicative Systems
[ PS ] [ DVI ] [ PDF ]
(5) (with Karen Yeats)
Admissible Dirichlet Series
[ PS ] [ DVI ] [ PDF ]

Jason's Homepage J. Bell's Publication List

Karen's Homepage K. Yeat's Publication List

Cameron Stewart's lecture notes on Number Theory