Prof. R. C. Vaughan FRS 
- Room No : 335 McAllister
- Telephone No. : +1 814 865-3583
- E-Mail Address : rvaughan AT math DOT psu
DOT edu
Research Interests :
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 "smooth numbers", i.e. numbers without large
prime factors, 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.
Publications
Some
Photographs
Some Quotations
Number
Theory Seminar
Math 401 Spring 2013
Math 421 Fall 2004
Math 465 Spring 2013
Math 467 Fall 2011
Math 568
Spring 2012
Math 571 Fall
2012
Math 597e Spring 2008
Math 567 Fall 2008
Math 504 Spring 2009
Math 572
Spring 2010
Lagrange's four
square theorem
Modular forms
I
Remarks
on the Selberg Sieve
The large
sieve and Bombieri's theorem Modular forms
II The Goldston,
Pinzt, Yilidirim theorem
Dirichlet's
theorem and Farey fractions
Continued
fractions The Geometry of
Numbers
Basic
Transcendence theory
Uniform
distribution Inhomogeneous
approximation