Expected number of real zeros of random Taylor Series

Hendrik Flasche, Zakhar Kabluchko

Let ${\xi }_0,{\xi }_1,\dots$ be i.i.d. random variables with zero mean and unit variance. Consider a random Taylor series of the form $f(z)={\sum }_{k=0}^{\infty }{\xi }_k{c}_k{z}^k$, where $c_0,c_1,\…