Level curves of rational functions and unimodular points on rational curves
Number Theory
2018-05-18 v2
Abstract
We obtain an improvement and broad generalisation of a result of N. Ailon and Z. Rudnick (2004) on common zeros of shifted powers of polynomials. Our approach is based on reducing this question to a more general question of counting intersections of level curves of complex functions. We treat this question via classical tools of complex analysis and algebraic geometry.
Keywords
Cite
@article{arxiv.1805.02913,
title = {Level curves of rational functions and unimodular points on rational curves},
author = {Fedor Pakovich and Igor E. Shparlinski},
journal= {arXiv preprint arXiv:1805.02913},
year = {2018}
}