On asymptotic behavior of the Taylor coefficients of algebraic functions (Q1920827)

The author studies the asymptotic behaviour of Taylor coefficients of algebraic functions of one and several variables. The main result of this paper is the following Theorem 5. If an algebraic function belongs to the class of Hölder continuous functions with exponent 1/2 on the closed unit bidisk \(\overline U^2\) and its singular set intersects \(\overline U^2\) only at finitely many points and its smooth near them, then the series composed of the moduli of the Taylor coefficients of this function converges. For any smaller Hölder exponent there exists an algebraic function for which the indicated series diverges.