International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 5, Pages 335-342

Mean number of real zeros of a random hyperbolic polynomial

J. Ernest Wilkins Jr.

Department of Mathematics, Clark Atlanta University, Atlanta 30314, GA, USA

Received 25 March 1998

Copyright © 2000 J. Ernest Wilkins. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Consider the random hyperbolic polynomial, f(x)=1pa1coshx++np×ancoshnx, in which n and p are integers such that n2,p0, and the coefficients ak(k=1,2,,n) are independent, standard normally distributed random variables. If νnp is the mean number of real zeros of f(x), then we prove that νnp=π1logn+O{(logn)1/2}.