On the convex hull of the points on multivariate modular hyperbolas

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• 作者：Igor E. Shparlinski ^{igor.shparlinski@unsw.edu.au" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11D79 ; 11H06
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：171
• 期：Complete
• 页码：71-78
• 全文大小：253 K

文摘

Given integers a  , m≥1$m\ge 1$ with gcd⁡(a,m)=1$\gcd (a,m)=1$ and s≥2$s\ge 2$, let H_s(a,m)${\mathcal{H}}_s(a,m)$ be the following set of integral points We obtain upper bounds on the number of vertices of the convex hull of H_s(a,m)${\mathcal{H}}_s(a,m)$. These bounds generalise those known for s=2$s=2$, although our approach is different.