Bivariate Factorizations via Galois Theory, with Application to Exceptional Polynomials |
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| Authors: | Michael Zieve |
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| Institution: | Department of Mathematics, University of Southern California, Los Angeles, California, 90089 |
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| Abstract: | We present a method for factoring polynomials of the shapef(X) − f(Y), wherefis a univariate polynomial over a fieldk. We then apply this method in the case whenfis a member of the infinite family of exceptional polynomials we discovered jointly with H. Lenstra in 1995; factoringf(X) − f(Y) in this case was posed as a problem by S. Cohen shortly after the discovery of these polynomials. |
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