# Virginia State University

Title: A Study of Bernstein Inequality for Self Reciprocal Polynomials of Degree Two and Related Subclasses

Director(s): Dawit Haile

Email: dhaile@vsu.edu

Dates of Program: May 21 - June 30, 2007

Summary: Denote the class of all algebraic polynomials of degree at most n by Pn. It is well known from Bernstein's Theorem that . Equality holds if and only if p(z) = czn, c is a constant.

This inequality has been improved under several kinds of restrictions. Consider a subclass consisting of all polynomials which has the property p(z) = znp(1/z). The question is if , what is the best estimate of in terms of ?

Using basic results from Complex Analysis and knowledge of Trigonometry and Calculus, students will explore the case when n = 3. They will also give an alternative proof for the known case when n = 2.

Student Researchers Supported by MAA:

• Aaron Sturgis
• Andrea Sims
• Merlin Woodlin

Program Contacts:

Bill Hawkins
MAA SUMMA
bhawkins@maa.org
202-319-8473

Michael Pearson
MAA Programs & Services
pearson@maa.org
202-319-8470