Mathematical Research Letters
Volume 3 (1996)
On the number of zeros of analytic functions in a neighborhood of a Fuchsian singular point with real spectrum
Pages: 359 – 372
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.