Moments of L-functions and Random Matrix Theory, Mathematics - MPhil/PhD (Funded) Ref: 3004

About the award

The University of Exeter’s College of Engineering, Mathematics and Physical Sciences, is inviting applications for a fully-funded PhD studentship to commence in February 2018 or as soon as possible thereafter.  For eligible students the studentship will cover UK/EU tuition fees plus an annual tax-free stipend of at least £14,553 for 3.5 years full-time, or pro rata for part-time study.  The student would be based in Exeter in the College of Engineering, Mathematics and Physical Sciences at the Streatham Campus in Exeter.


Mathematics, Streatham Campus, CEMPS, Exeter

Academic Supervisors:
Dr Julio Andrade, University of Exeter
Professor Andreas Langer, University of Exeter

Project Description:
It is an important topic in analytic number theory to understand the moments of the Riemann zeta-function and other L-functions. In this project the student will study the connections involving moments of L-functions in families with random matrix theory. Specifically, the main subject of study will be the Euler-Hadamard hybrid formula. Other topics include the study of distribution of zeros of L-functions such as one-level density and pair correlation. For the final parts of the project the student will focus on function field analogues of the Hybrid formula for different families of L-functions over function fields of higher genus.

This award provides annual funding to cover UK/EU tuition fees and a tax-free stipend.  For students who pay UK/EU tuition fees the award will cover the tuition fees in full, plus at least £14,553 per year tax-free stipend.  Students who pay international tuition fees are eligible to apply, but should note that the award will only provide payment for part of the international tuition fee and no stipend. 

The studentship will be awarded on the basis of merit for 3.5 years of full-time study to commence in February 2018 and is subject to confirmation of funding.

Entry requirements:
Applicants for this studentship must have obtained, or be about to obtain, a First or Upper Second Class UK Honours degree, or the equivalent qualifications gained outside the UK, in an appropriate area of science or technology. It is desirable (but not essential) to have some research experience in mathematics and a master’s degree in Mathematics and/or allied fields.   
If English is not your first language you will need to have achieved at least 6.0 in IELTS and no less than 6.0 in any section by the start of the project.  Alternative tests may be acceptable (see


Application deadline:12th January 2018
Number of awards:1
Value:£14,553 for 3.5 years
Duration of award:per year
Contact: Postgraduate Research

How to apply

In the application process you will be asked to upload several documents. 
• CV
• Letter of application (outlining your academic interests, prior research experience and reasons for wishing to undertake the project).
• Transcript(s) giving full details of subjects studied and grades/marks obtained (this should be an interim transcript if you are still studying)
• Names of two referees familiar with your academic work. You are not required to obtain references yourself. We will request references directly from your referees if you are shortlisted.
• If you are not a national of a majority English-speaking country you will need to submit evidence of your proficiency in English
The closing date for applications is midnight on 12/01/2018.  Interviews will be held on the University of Exeter Streatham Campus the week commencing 22/01/2018.
If you have any general enquiries about the application process please email or phone +44 (0)1392 722730.  Project-specific queries should be directed to the main supervisor.