Abstract
Let be a homogeneous form of degree , and let denote the singular locus of the affine variety . In this paper, we prove the existence of integer solutions with prime coordinates to the equation provided that F satisfies suitable local conditions and . Our result improves on what was known previously due to Cook and Magyar, which required to be an exponential tower in d.
Citation
Shuntaro Yamagishi. "Diophantine equations in primes: Density of prime points on affine hypersurfaces." Duke Math. J. 171 (4) 831 - 884, 15 March 2022. https://doi.org/10.1215/00127094-2021-0023
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