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Department of Mathematics

Number theory

Number theory is an ancient area of mathematics involving the study of integers, well-known for the simplicity of its statements and beauty of its proofs.

Academic staff

Heilbronn Fellow

Dame Kathleen Ollerenshaw, Turing and Neumann Fellows

The University of Manchester has a long history of research in number theory, dating back at least to 1907 when Littlewood was appointed as the Richardson Lecturer in Mathematics. Mordell moved to Manchester in 1920, and while in Manchester proved his famous theorem concerning the finite generation of the group of rational points on an elliptic curve. In 1923, Mordell was appointed to the Fielden Chair in Pure Mathematics, and attracted other eminent number theorists including Davenport and Mahler.

It was also at Manchester where Alan Turing invented and implemented the first computer algorithm for searching for zeros of the Riemann zeta function. Variants of Turing’s method are still used to this day. More recent number theorists at Manchester include Sir Martin Taylor.

After a brief hiatus, the number theory group has been recently reformed. We have a very active research group, with our research themes including:

  • Diophantine and arithmetic geometry
  • Diophantine approximation
  • The theory of zeta-functions and L-functions
  • The distribution of class numbers
  • Analytic number theory over number fields and function fields