Document Type

Conference Proceeding

Publication Date

2004

Publication Title

CNTA-VII: CRM Proceedings & Lecture Notes

Abstract

We describe a general three step method for constructing number fields with Lie-type Galois groups and discriminants factoring into powers of specified primes. The first step involves extremal solutions of the matrix equation ABC = I. The second step involves extremal polynomial solutions of the equation A(x) + B(x) + C(x) = 0. The third step involves integer solutions of the generalized Fermat equation axp + byq + czr = 0. We concentrate here on details associated to the third step and give examples where the field discriminants have the form ±2a3b .

Volume

36

First Page

237

Last Page

267

Comments

First published in CNTA-VII: CRM Proceedings and Lecture Notes 36 (2004), published by the American Mathematical Society and Centre de Recherches Mathématiques. © 2004 American Mathematical Society.

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