Polynomial Equations in Subgroups and Applications
Number Theory
2020-05-13 v1
Abstract
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 modulo a prime .
Keywords
Cite
@article{arxiv.2005.05315,
title = {Polynomial Equations in Subgroups and Applications},
author = {Sergei V. Konyagin and Igor E. Shparlinski and Ilya V. Vyugin},
journal= {arXiv preprint arXiv:2005.05315},
year = {2020}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1711.05335