Mathematical Research Letters

Volume 3, Issue 3, May 1996 pp. 359-372.

On the number of zeros of analytic functions in a neighborhood of a Fuchsian singular point with real spectrum

Authors: M. Roitman and S. Yakovenko
Author institution: Yale University, and Weizmann Institute of Science

Summary: Consider a linear differential equation of some order $n$ with coefficients analytic in the unit disk. Assuming that the equation has a unique Fuchsian singular point at $z=0$, and all roots of the corresponding indicial equation are real, we establish an upper bound for the number of zeros of any solution of this equation in any sector with the vertex at $z=0$. This upper bound is in some sense linear in the magnitude of the coefficients of the equation.

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