Level curves of rational functions nd unimodular points on rational curves

Fedor Pakovich; Igor E. Shparlinski

doi:10.1090/proc/14928

Level curves of rational functions nd unimodular points on rational curves

Fedor Pakovich
, Igor E. Shparlinski

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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.

Original language	English
Pages (from-to)	1829-1833
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	148
Issue number	5
DOIs	https://doi.org/10.1090/proc/14928
State	Published - 1 Jan 2020

Keywords

Ailon and Rudnick theorem
Blaschke product
Unimodular points

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/proc/14928

Cite this

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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.",

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AB - 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.

KW - Ailon and Rudnick theorem

KW - Blaschke product

KW - Unimodular points

UR - https://www.scopus.com/pages/publications/85083108717

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DO - 10.1090/proc/14928

M3 - Article

AN - SCOPUS:85083108717

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 5

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Level curves of rational functions nd unimodular points on rational curves

Abstract

Keywords

ASJC Scopus subject areas

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