Mahler Measure and Weber's Class Number Problem

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• Jack Lamplugh University of Cambridge
• Friday 18 October 2013, 15:00-16:00
• CMS, MR5.

If you have a question about this talk, please contact Julian Brough.

It has been an open problem for over 200 years as to whether there are infinitely many number fields of class number 1. Over 100 years ago, Weber studied the class numbers of the layers of cyclotomic Z_2 extension of the rationals and showed that the first 3 layers have class number one. Recently much progress has been made by Japanese mathematicians indicating that perhaps all layers of all cyclotomic Z_p extensions for all primes p have class number 1. In my talk I will explain these results (and what the cyclotomic Z_p of the rationals is!) and talk about my work in extending this to non-cyclotomic Z_p extensions

This talk is part of the Junior Algebra/Logic/Number Theory seminar series.

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