Level curves of rational functions and unimodular points on rational curves

Pakovich, Fedor; Shparlinski, Igor

doi:10.1090/proc/14928

Level curves of rational functions and unimodular points on rational curves
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by Fedor Pakovich and Igor E. Shparlinski PDF

Proc. Amer. Math. Soc. 148 (2020), 1829-1833 Request permission

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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