Abstract: 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. This leads to the study of primes in arithmetic progressions to large moduli and automorphic analogue of the Titchmarsh divisor problems. We also consider the number of representations of an integer as the sum of a smooth number and two almost prime squares. This is based on joint work with Assing-Blomer and Blomer-Rydin Myerson.
https://illinois.zoom.us/j/84027824197?pwd=TzkyUGRpeDZIcnVxTnpvVEVyLytXUT09
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