Automorphic forms, spectral theory and Kloosterman sums

A series of four lectures to be given by Professor Roger Baker (Brigham Young University), November 1st-4th, 2004 at the (new) University of Manchester.

Abstract: Analytic number theory usually requires analysis that is very accessible, even 'easy'. For example, when Fourier analysis is employed, the deepest results used are Poisson's summation formula and Plancherel's theorem. In the case of Kloosterman sums, the analysis that can be used to obtain valuable results is much deeper. The spectral theory of automorphic forms must be deployed, and a detailed picture of the automorphic forms appearing in the expansions is needed.
In these four lectures, totalling 6 hours, we explain the usefulness of Kloosterman sums in analytic number theory, show how these sums occur in
expansions of automorphic forms, and examine the analytic tools (including Kuznetsov's formulae) that paved the way for some recent applications to prime number theory. Although there is a large overlap with the analysis underlying Selberg's trace formula, we shall not have time to pursue this.
The presentation will be accessible to beginning graduate students.

The timetable is 2.00-3.30, Monday 1st - Thursday 4th November. The talks will be followed by tea and coffee.

The talks will be held in room M16 in the MSS building, Department of Mathematics, North Campus, University of Manchester (formerly UMIST).

A map of the campus can be found here, where the MSS building is number 22.

If you have any enquiries please contact Dr. M. D. Coleman, or 0161 200 3649.