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.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/246