Expected number of real zeroes of random Taylor series
Let [Formula: see text] be i.i.d. random variables with zero mean and unit variance. Consider a random Taylor series of the form [Formula: see text] where [Formula: see text] is a real sequence such that [Formula: see text] is regularly varying with index [Formula: see text] where [Formula: see text] We prove that [Formula: see text] where [Formula: see text] denotes the number of real zeroes of [Formula: see text] in the interval [Formula: see text]
Communications in Contemporary Mathematics