Geodesic
Zeroes of Polynomials With Prime Inputs and Schmidt’s $h$-invariant
Canadian journal of mathematics, Tome 72 (2020) no. 3, pp. 805-833

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DOI

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.
DOI : 10.4153/S0008414X19000026
Mots-clés : Circle method, h-invariant, Hardy–Littlewood, prime numbers 
Xiao, Stanley Yao; Yamagishi, Shuntaro. Zeroes of Polynomials With Prime Inputs and Schmidt’s $h$-invariant. Canadian journal of mathematics, Tome 72 (2020) no. 3, pp. 805-833. doi: 10.4153/S0008414X19000026
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     title = {Zeroes of {Polynomials} {With} {Prime} {Inputs} and {Schmidt{\textquoteright}s} $h$-invariant},
     journal = {Canadian journal of mathematics},
     pages = {805--833},
     year = {2020},
     volume = {72},
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     doi = {10.4153/S0008414X19000026},
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