Level curves of rational functions and unimodular points on rational\n curves

2018/05/08 by Fedor Pakovich, Pakovich, Fedor, Igor E. Shparlinski +1
Computer Science · Mathematics · #Advanced Mathematical Identities #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1805.02913

openalex publication_date 2018/05/08 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We obtain an improvement and broad generalisation of a result of N. Ailon and\nZ. Rudnick (2004) on common zeros of shifted powers of polynomials. Our\napproach is based on reducing this question to a more general question of\ncounting intersections of level curves of complex functions. We treat this\nquestion via classical tools of complex analysis and algebraic geometry.\n

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