论文标题
亚组和应用中的多项式方程
Polynomial Equations in Subgroups and Applications
论文作者
论文摘要
我们获得了一个新的界限，以在有限领域的乘法亚组的coset中的多项式方程数限制，该方程概括了P. Corvaja和U. Zannier（2013）的先前结果。我们还获得了J. Bourgain，A。Gamburd和P. Sarnak（2016）和S. V. Konyagin，S。V。Makarychev，I。E。E. Shparlinski和I. V. Vyugin（2019）的最新结果有条件改善。
We obtain a new bound for the number of solutions to polynomial equations in cosets of multiplicative subgroups in finite fields, which generalises previous results of P. Corvaja and U. Zannier (2013). We also obtain a conditional improvement of recent results of J. Bourgain, A. Gamburd and P. Sarnak (2016) and S. V. Konyagin, S. V. Makarychev, I. E. Shparlinski and I. V. Vyugin (2019) on the structure of solutions to the reduction of the Markoff equation $x^2 + y^2 + z^2 = 3 x yz$ modulo a prime $p$.
