Albion College Mathematics and Computer Science Colloquium

 Title: The P2 + P problem and conjectures of Pólya Speaker: Stephanie Edwards Associate Professor Department of Mathematics Hope College Holland, Michigan Abstract: One of the problems stated in the Pólya and Szegö text from the early 1900's, "Aufgaben und Lehrsätze aus der Analysis," is: If P is a real polynomial with only real zeros, find the number of non-real zeros of P2 + P. If one removes the hypothesis that P has only real zeros, the problem becomes quite hard and was not solved until the 1980's. We will solve the P2 + P problem when P has only simple real zeros. Further, we will show how the problem can be restated in terms of the number of non-real zeros of the second derivative of a real entire function and discuss the research and progress which has been made in the area of distribution of zeros of real entire functions. Location: Palenske 227 Date: 11/5/2009 Time: 3:10

@abstract{MCS:Colloquium:StephanieEdwards:2009:11:5,
author  = "{Stephanie Edwards}",
title   = "{The P2 + P problem and conjectures of Pólya}",
address = "{Albion College Mathematics and Computer Science Colloquium}",
month   = "{5 November}",
year    = "{2009}"
}