Department of Mathematics, Royal Holloway, University of London, Egham Hill, Egham, Surrey

**Phone: **+44 1784 276582

The Number Theory Group at Royal Holloway has a wide range of interests. Research is carried out in many areas such as: additive and multiplicative number theory, sieve methods, Diophantine approximation, Diophantine equations, metric number theory, the circle method, exponential sums, Salem and Pisot numbers, Mahler measure, totally real algebraic integers, the Riemann Zeta-function, zeta functions of groups and rings, arithmetic groups, p-adic Lie groups and their representations.

Recent work of the group has included representations by quadratic forms, probabilistic Galois theory, random Diophantine problems, the distribution of Gaussian primes in narrow sectors or small circles, prime values of the integer parts of points on algebraic curves, prime values of polynomials, the prime k-tuple problem, work on pairing-friendly abelian varieties, Lehmer’s problem for reciprocal polynomials of integer symmetric matrices, the Schur-Siegel-Smyth trace problem, graph Salem numbers, and non-linear Diophantine approximation to complex numbers. There are regular seminars in these and related fields - contact Dr Rainer Dietmann for details.

For opportunities for postgraduate research in number theory please contact Dr Dietmann, Dr Klopsch or Dr McKee.

- Published
## Weak admissibility, primitivity, o-minimality, and Diophantine approximation

Research output: Contribution to journal › Article

- Forthcoming
## Sums of two numbers having only prime factors congruent to one modulo four

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

- Submitted
## A contraction theorem for the largest eigenvalue of a multigraph

Research output: Contribution to journal › Article

## Forms in many variables

Project: Research

## Representation zeta functions of arithmetic groups

Project: Research

ID: 24160