EPSRC DTP PhD studentship: Hybrid Euler-Hadamard Formula in Function Fields

Location: University of Exeter, Streatham Campus, Exeter, Devon

Project Description:
The proposed project is in number theory, an area of pure mathematics which is concerned with prime numbers and solutions to equations. It has long been understood in the field that there are strong analogies between number theory and the geometry of curves. As a deeper understanding of this analogy could have tremendous consequences, the search for a unified approach and the reinterpretation of geometric methods has been a source of inspiration and success for number theorists.

The main aim of the project is to extend the hybrid formula for function fields and to investigate moments of L-functions in this setting. The advantage here is that the hybrid formula will not be an approximation to L-functions but will be an exact formula since in this case the L-functions are polynomials.

The calculations involved in this project are subtle and important, and any small progress will enormously benefit the academic career of the student. The student will have contact with very recent research and will be able to interact with members in Exeter, Bristol and France.