doiSerbia

On a property of entire functions with almost negative zeros

Simić Slavko (Mathematical Institute SANU, Belgrade)

We give a generalization of well-known Valiron-Titchmarsh theorem on entire functions with negative zeros. Namely, we prove that (-1)plogP(r)ЄER[p,p+1] where P(r) denotes the canonical product of an entire function with genus p and almost negative zeros and ER is the class of extended regular variation.

Keywords: entire functions of finite order, almost negative zeros, extended regular variation