Title: | The P^{2} + 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 P^{2} + 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 P^{2} + 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 P^{2} + P problem and conjectures of Pólya}", address = "{Albion College Mathematics and Computer Science Colloquium}", month = "{5 November}", year = "{2009}" }