Geodesic
Square-free Values of Decomposable Forms
Canadian journal of mathematics, Tome 70 (2018) no. 6, pp. 1390-1415

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DOI

In this paper we prove that decomposable forms, or homogeneous polynomials $F\left( {{x}_{1}}\,,\,.\,.\,.\,,\,{{x}_{n}} \right)$ with integer coefficients that split completely into linear factors over $\mathbb{C}$ , take on infinitely many square-free values subject to simple necessary conditions, and they have $\text{deg}\,f\,\le \,2n\,+\mid 2$ for all irreducible factors $f$ of $F$ . This work generalizes a theorem of Greaves.
DOI : 10.4153/CJM-2017-060-4
Mots-clés : 11B05, square-free value, decomposable form, Selberg sieve 
Xiao, Stanley Yao. Square-free Values of Decomposable Forms. Canadian journal of mathematics, Tome 70 (2018) no. 6, pp. 1390-1415. doi: 10.4153/CJM-2017-060-4
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     author = {Xiao, Stanley Yao},
     title = {Square-free {Values} of {Decomposable} {Forms}},
     journal = {Canadian journal of mathematics},
     pages = {1390--1415},
     year = {2018},
     volume = {70},
     number = {6},
     doi = {10.4153/CJM-2017-060-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2017-060-4/}
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