Hardy-Littlewood problems with almost primes
Heilbronn Number Theory Seminar
26th January 2022, 4:00 pm – 5:00 pm
The Hardy-Littlewood problem asks for the number of representations of an integer as the sum of a prime and two squares. We consider the Hardy-Littlewood problem where the two squares are restricted to almost primes. A lower bound of the expected order of magnitude can be obtained under the generalized Riemann Hypothesis for Dirichlet L-functions. We also discuss the problem of writing an integer as the sum of a smooth number and two almost prime squares.