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math.CV2025
Sharp bounds for some segments of bounded power series
Leonid V. Kovalev
We obtain sharp upper bounds for three-term segments of a bounded power series. Along the way we show that the Taylor polynomials of a certain algebraic function do not vanish in t…
math.CV2024
A sharp bound on the number of self-intersections of a trigonometric curve
Sergei Kalmykov, Leonid V. Kovalev
We obtain a sharp bound on the number of self-intersections of a closed planar curve with trigonometric parameterization. Moreover, we show that a generic curve of this form is nor…