Level curves of rational functions and unimodular points on rational curves
Copyright policy )Level curves of rational functions and unimodular points on rational curves
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.
- UNSW Sydney Australia
- Ben-Gurion University of the Negev Israel
Mathematics - Number Theory, 4904 Pure Mathematics, Polynomials in real and complex fields: location of zeros (algebraic theorems), Blaschke products, unimodular points, anzsrc-for: 0101 Pure Mathematics, anzsrc-for: 4904 Pure Mathematics, 510, 004, anzsrc-for: 49 Mathematical Sciences, Ailon and Rudnick theorem, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), 49 Mathematical Sciences, FOS: Mathematics, Number Theory (math.NT), Blaschke product, Exponential Diophantine equations
Mathematics - Number Theory, 4904 Pure Mathematics, Polynomials in real and complex fields: location of zeros (algebraic theorems), Blaschke products, unimodular points, anzsrc-for: 0101 Pure Mathematics, anzsrc-for: 4904 Pure Mathematics, 510, 004, anzsrc-for: 49 Mathematical Sciences, Ailon and Rudnick theorem, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), 49 Mathematical Sciences, FOS: Mathematics, Number Theory (math.NT), Blaschke product, Exponential Diophantine equations
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