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The P^2+P’ problem and George Polya

  • Thursday, September 19, 2019
  • 3:40 PM–4:30 PM
  • North Hall 276

Stephanie Edwards, Hope College

Many open problems in entire function theory, specifically, the distribution of zeros of real entire functions, can be tracked back to work by George Polya.  One of these such problems was stated in a Polya and Szego text from the early 1900’s:  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 difficult and was not solved until the 1980’s.  We will discuss a simple solution to the problem, look at natural questions that arise from the problem and discuss some open questions which have their roots in Polya.

Refreshments precede the talk at 3:30 p.m. in NH 282.

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