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Additive problems with almost prime squares

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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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