Regular Primes

Paulo Ribenboim
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Paulo Ribenboim: Jeffery Hall Queen’s University, Department of Mathematics and Statistics

Chapter Lecture VI in 13 Lectures on Fermat’s Last Theorem, 1979, pp 93-113 from Springer

Abstract: Abstract To utilize the force of Kummer’s main theorem, it is imperative to determine when a prime p is regular. In theory, at least, this is simple. All one needs to do is to compute the class number of the cyclotomic field K p = ℚ(ζ p ), where ζ p is a primitive pth root of 1. And so Kummer began by discovering formulas for the class number. However, it soon became apparent that the computations involved were much too difficult, and other more suitable criteria for regularity were needed. These were also discovered by Kummer.

Keywords: Prime Ideal; Class Number; Bernoulli Number; Arithmetic Property; Principal Character (search for similar items in EconPapers)
Date: 1979
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DOI: 10.1007/978-1-4684-9342-9_6

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