### Hardy-Littlewood problems with almost primes

Heilbronn Number Theory Seminar

26th January 2022, 4:00 pm – 5:00 pm

Online, Zoom

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.

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