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Additive problems with almost prime squares

Posted in
Valentin Blomer
Universität Bonn
Wed, 07/12/2022 - 14:30 - 15:30
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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