@article{c652ae0ea7d4497799b93d8f52176b33,

title = "Level curves of rational functions nd unimodular points on rational curves",

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 = "Ailon and Rudnick theorem, Blaschke product, Unimodular points",

author = "Fedor Pakovich and Shparlinski, {Igor E.}",

note = "Funding Information: Received by the editors May 16, 2018, and, in revised form, July 29, 2018. 2010 Mathematics Subject Classification. Primary 11D61, 12D10, 30C15, 30J10. Key words and phrases. Unimodular points, Ailon and Rudnick theorem, Blaschke product. The work of the second author was supported in part by the Australian Research Council Grants DP170100786 and DP180100201. Publisher Copyright: {\textcopyright} 2020 American Mathematical Society. All rights reserved.",

year = "2020",

month = jan,

day = "1",

doi = "10.1090/proc/14928",

language = "English",

volume = "148",

pages = "1829--1833",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "5",

}