Almost Prime Coordinates for Anisotropic and Thin Pythagorean Orbits

preprint2014arXivOpen access

Abstract

We make an observation which doubles the exponent of distribution in certain Affine Sieve problems, such as those considered by Liu-Sarnak, Kontorovich, and Kontorovich-Oh. As a consequence, we decrease the known bounds on the saturation numbers in these problems.

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