Random polynomials: Central limit theorems for the real roots

The number of real roots has been a central subject in the theory random polynomials and functions since fundamental papers Littlewood, Offord, Kac 1940s. main task here is to determine limiting distribution this variable. In 1974, Maslova famously proved limit theorem (CLT) for polynomials. It remained only available more than four decades. paper, using new approach, we derive general CLT large class with coefficients growing polynomially. Our result both generalizes strengthens Maslova’s theorem.