Room No : 335 McAllister
E-Mail Address : rcv4 AT psu DOT edu
My main research is in
number theory, that is, the study of the properties of the whole
numbers, especially by the use of analytic techniques.
Particular subjects of interest are Waring's problem, the
Goldbach problem, the Hardy-Littlewood method, the use of
y-factorable numbers, i.e. numbers with no prime factors
exceeding y, the distribution of prime numbers, exponential sums
over integer sequences such as the sequence of primes,
properties of the Riemann zeta-function and Dirichlet
L-functions and diophantine approximation.
It can be of no
practical use to know that π is irrational, but if we
can know, it surely would be intolerable not to know.
E. C. Titchmarsh (1899-1963)
Publications
Some Photographs
Some Quotations
Pronunciation of
British Names
Obituary of Thomas Vaughan
Tribute by
Robert Reeves
Algebra
and Number Theory Seminar 2007-, Spring 2007, Fall 2006, Spring 2006, Fall 2004, Spring 2004, Spring 2003, Fall 2002, Spring 2002, Fall 2001, Spring 2001, Fall 2000
A Course of Elementary Number Theory
An
Introduction to Analysis
An Introduction to
Factorization and Primality Testing
These are books based on the elementary number theory and
introductory analysis courses I have taught over nearly fifty
years at Imperial College London and Penn State University.
I don't think publishers should charge huge amounts for what can
be produced with very little effort.
Math 401
Spring 2024 Math 421 Fall
2004 Math 465 Spring
2021 Math 467 Fall 2023
Math
504 Spring 2009
Math 568
Spring 2020 Math 571 Spring
2023 Math 597e Spring 2008 Math 597b
Spring 2015
Lagrange's 4 square theorem Remarks on the Selberg
Sieve
Jarnik's theorem on
integer points on curves
Dirichlet's theorem and Farey fractions
Modular forms I
The large sieve
Brandon Hanson's notes on
Stepanov-Burgess Continued fractions
Modular forms II
The Bombieri-A. I. Vinogradov theorem
Khinchin
heuristics
The Geometry of Numbers
Density and sum
sets
The
Goldston, Pintz, Yilidirim theorem Inhomogeneous
approximation
A theorem of E. M. Wright on Waring's
Problem
Rouché's Theorem
Uniform distribution
Basic Transcendence
theory
A survey of the Montgomery_Hooley Theorem
The Basel Problem