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Distribution of Values of L-functions and Modular Forms

  • Full or part time
  • Application Deadline
    Applications accepted all year round
  • Competition Funded PhD Project (Students Worldwide)
    Competition Funded PhD Project (Students Worldwide)

Project Description

The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing either in September 2020 for students seeking funding, or in January 2020 or April 2020 for self-funded students. The deadline for funded applications is the 31st of January 2020. The deadline for China Scholarship Council Scheme applications is 12th January 2020.

This project will be supervised by Dr Steve Lester.

L-functions and automorphic forms appear prominently in modern number theory and also arise in other areas of mathematics. The analytic properties of these functions are closely related to arithmetic problems involving the distribution of the prime numbers, lattice points, and structure of elliptic curves. For instance, Millennium prize problems such as the Generalised Riemann Hypothesis and Birch and Swinnerton-Dyer Conjecture are directly related to the theory of these functions.

This project aims to further understand the analytic behaviour of L-functions and automorphic forms, with applications to problems arising in number theory or mathematical physics. Specific problems will follow the interests of the student and possible topics include: the distribution of zeros of Hecke cusp forms, moment estimates for families of L-functions, and the behaviour of Fourier coefficients of automorphic forms.

Part of the project could potentially explore profound connections between $L$-functions and modular forms to questions in quantum chaos, which is an sub-field of mathematical physics which studies the quantum dynamics of classically chaotic systems. This is an especially exciting area of study that is still quite mysterious. Fascinatingly, much progress has been made in special arithmetic settings in which automrophic forms and $L$-functions play a prominent role.

Previous exposure to analytic number theory or,algebraic number theory would be advantageous, however not necessary and may be learned during PhD research. Background in real and complex analysis along with probability theory and harmonic analysis would be desirable.

The application procedure is described on the School website. Applicants interested in the full funding will have to participate in a highly competitive selection process. For further inquiries please contact Dr Steve Lester at .

Funding Notes

This project is eligible for full funding, including support for 3.5 years’ study, additional funds for conference and research visits and funding for relevant IT needs.

This project can be undertaken as a self-funded project. Self-funded applications are accepted year-round for a January, April or September start.

We welcome applicants through the China Scholarship Council Scheme (deadline for applications 12th January 2020).

The School of Mathematical Sciences is committed to the equality of opportunities and to advancing women’s careers. As holders of a Bronze Athena SWAN award we offer family friendly benefits and support part-time study.

Related Subjects

How good is research at Queen Mary University of London in Mathematical Sciences?

FTE Category A staff submitted: 34.80

Research output data provided by the Research Excellence Framework (REF)

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