Analytic Computation of the Prime -Counting Function

Our work resolves many issues left untreated in the original paper by Lagarias and Odlyzko and makes several original contributions---some of which have applications in other areas. In this dissertation we: (1) introduce a kernel function which appears to be more effective than the one suggested by Lagarias and Odlyzko; (2) perform a careful analysis of various sources of truncation error; (3) give choices of parameters which bound the truncation error while keeping computation to a minimum; (4) develop two new methods for enumerating primes in intervals, which require much less memory than previously known sieving methods and which are much faster than methods which test primality of single numbers; (5) describe a new method for computing zeta(s) which gives more accurate values with less complexity than classical methods.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Galway, William Floyd

Contributors dc:contributor

• Diamond, Harold G.

• Computer Science

Language dc:language

eng

Identifier

(MiAaPQ)AAI3153295

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86834