1 results
Zeroes of Polynomials With Prime Inputs and Schmidt’s
$h$-invariant
- Part of
-
- Journal:
- Canadian Journal of Mathematics / Volume 72 / Issue 3 / June 2020
- Published online by Cambridge University Press:
- 07 February 2019, pp. 805-833
- Print publication:
- June 2020
-
- Article
- Export citation
-
In this paper we show that a polynomial equation admits infinitely many prime-tuple solutions, assuming only that the equation satisfies suitable local conditions and the polynomial is sufficiently non-degenerate algebraically. Our notion of algebraic non-degeneracy is related to the
$h$-invariant introduced by W. M. Schmidt. Our results prove a conjecture by B. Cook and Á. Magyar for hypersurfaces of degree 3.
