Additive problems and exponential sums over smooth numbers

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• Adam Harper (University of Cambridge)
• Tuesday 01 December 2015, 14:15-15:15
• MR13.

If you have a question about this talk, please contact Jack Thorne.

A number is said to be y-smooth if all of its prime factors are at most y. Exponential sums over the y-smooth numbers less than x have been widely investigated, but existing results were weak for y too small compared with x. For example, if y is a power of log x then existing results were insufficient to study three variable additive problems involving smooth numbers (e.g. problems analogous to the three variable Goldbach conjecture), except by assuming conjectures like the Generalised Riemann Hypothesis.

I will try to describe my work on bounding mean values of exponential sums over smooth numbers, which allows an unconditional treatment of three variable additive problems even with y a (large) power of log x. There are connections with restriction theory and additive combinatorics.

This talk is part of the Number Theory Seminar series.

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