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arXiv · 1512.01258

Zeroes of polynomials with prime inputs and Schmidt's $h$-invariant

Stanley Yao Xiao·Shuntaro Yamagishi
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Abstract

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 of B. Cook and Á. Magyar \cite{CM} for hypersurfaces of degrees $2$ and $3$.

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Stanley Yao Xiao, Shuntaro Yamagishi. 2018-03-28. Zeroes of polynomials with prime inputs and Schmidt's $h$-invariant. https://doi.org/10.4153/s0008414x19000026

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