Why are bilinear forms important in analytic number theory?

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• Adam Harper, Cambridge
• Friday 11 November 2011, 16:00-17:00
• MR15, CMS.

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

Tea in Pavilion E from 3.30

Many problems in number theory involve obtaining good estimates for sums over primes, sums weighted by arithmetic functions, or similar. One possible approach to this, which is often branded as “the method of Type II sums”, involves somehow reorganising the sum of interest so that it has a bilinear shape. In this seminar I will try to explain some examples where this technique is useful. The talk will be almost completely expository, but amongst other things I will present a simpler proof of a recent bilinear sums result of Bourgain, Sarnak and Ziegler. I may also make a (tenuous) connection with some of my recent work on S-unit equations.

This talk is part of the Discrete Analysis Seminar series.

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