Research in Number Theory

The number Theory group at Manchester currently has two members, whose combined research interests span a wide range of topics in algebraic and analytic number theory.

Research areas

Algebraic Number Theory:

Prof. Taylor's research has mainly concerned the Galois sructures and symmetries of algebraic tructures, and their relationship to the behaviour to L- functions. He is particularly interested in Algebraic K- theory, Arithmetic Aspects of representation theory, and quadratic and hermitian forms. Over recent years he has increasingly become interested in arithmetic geometry, in particular, elliptic curves and tames covers of arithmetic varieties.

Analytic Number Theory:

Dr. Coleman's main research interests concern the area between analytic and algebraic number theory. Going back to Hecke in the early part of the century it was found that the analytic properties of various L-functions, defined in the manner of the Riemann zeta-function, could give information about the distribution of prime ideals. Information not only on the distribution of the norms of the ideals, which would in fact arise from the Dedekind zeta-function, but also the so-called "angular distribution". Using this we can study, for instance, the distribution of Gaussian primes in the plane.

Dr. Coleman is also interested in Sieve methods and the study of arithmetic functions.

Members of staff involved: