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- W2738892011 abstract "We use Vaughan's variation on Vinogradov's three-primes theorem to prove Zariski-density of prime points in several infinite families of hypersurfaces, including level sets of some quadratic forms, the Permanent polynomial, and the defining polynomials of some pre-homogeneous vector spaces. Three of these families are instances of a conjecture by Bourgain, Gamburd and Sarnak regarding prime points in orbits of simple algebraic groups. Our approach is based on the formulation of a general condition on the defining polynomial of a hypersurface, which suffices to guarantee that Zariski-density of prime points is equivalent to the existence of an odd point." @default.
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- W2738892011 date "2017-07-15" @default.
- W2738892011 modified "2023-09-27" @default.
- W2738892011 title "Prime Points in Orbits: Some Instances of the Bourgain-Gamburd-Sarnak Conjecture" @default.
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