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Speaker:

Valentin Blomer
Affiliation:

Universität Bonn
Date:

Wed, 07/12/2022 - 14:30 - 15:30
Location:

MPIM Lecture Hall
Parent event:

Number theory lunch seminar Contact: Pieter Moree

The prototype equation of this talk is n = p + x

2 + y 2, considered first by Hardy and Littlewood and later by Hooley and Linnik. It is shown that this equation and variations of it have the expected number of representations with x and y being almost primes (i.e. having a bounded number of prime factors).The proof involves a mix of algebraic number theory, algebraic geometry to estimate multiple exponential sums, automorphic forms and analytic number theory. The method can also handle the case when x and y are smooth numbers. This is joint work with L. Grimmelt, J. Li and S. Myerson.

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