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.
subjects of interest are Waring's problem, the Goldbach problem,
Hardy-Littlewood method, the use of "smooth numbers", i.e.
numbers without large prime factors, the distribution of prime
numbers, exponential sums over integer sequences such as the
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)
Some Quotations Pronunciation of British Names
Number Theory Seminar
Math 401 Spring 2018 Math 421 Fall 2004 Math 465 Spring 2013 Math 467 Fall 2017
Math 567 Fall 2008 Math 568 Spring 2018 Math 571 Fall 2016 Math 597e Spring 2008
Math 504 Spring 2009 Math 572 Spring 2010 Math 597b Spring 2015
Lagrange's four square
Modular forms I
Remarks on the Selberg
Hanson's notes on Stepanov-Burgess
The large sieve and Bombieri's theorem Modular forms II The Goldston, Pintz, Yilidirim theorem Jarnik's theorem on integer points on convex curves
Dirichlet's theorem and Farey fractions Continued fractions The Geometry of Numbers
Basic Transcendence theory Uniform distribution Inhomogeneous approximation
Density and sum sets Khinchin heuristics Rouché's Theorem