On a conjecture of Serre

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• Lillian Pierce (Oxford)
• Wednesday 08 May 2013, 16:00-17:00
• MR4, CMS.

If you have a question about this talk, please contact Ben Green.

A conjecture of Serre concerns the number of rational points of bounded height on a finite cover of projective space. This talk will describe joint work with Roger Heath-Brown that verifies Serre’s conjecture in certain special cases, and even improves on it in sufficiently high dimensions. The problem boils down to giving a good upper bound for the number of perfect power values of a polynomial in many variables with integer coefficients. Such an upper bound is obtained via a combination of techniques in analytic number theory; we will highlight the power sieve, the q-analogue of van der Corput’s method, and an arithmetic version of Poisson summation.

This talk is part of the Discrete Analysis Seminar series.

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