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
A Course of Elementary Number Theory
This is a book based on the elementary number theory 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 2023
Fall 2004 Math 465 Spring 2021
Math 467 Fall 2017
Math 567 Fall 2008
568 Spring 2020
Math 571 Spring 2023 Math 597e Spring 2008 Math 504 Spring 2009 Math 572 Spring 2010 (old syllabus) Math 597b Spring 2015
Lagrange's 4 square theorem Remarks on the
on integer points on curves
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