Dirichlet L-Series and Class Number Formulas

Yuri F. Bilu, Yann Bugeaud and Maurice Mignotte
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Yuri F. Bilu: University of Bordeaux and CNRS, Institute of Mathematics of Bordeaux
Yann Bugeaud: University of Strasbourg and CNRS, IRMA, Mathematical Institute
Maurice Mignotte: University of Strasbourg and CNRS, IRMA, Mathematical Institute

Chapter Chapter 5 in The Problem of Catalan, 2014, pp 49-63 from Springer

Abstract: Abstract In this chapter we use analytic tools (the Dirichlet L-series and the Dedekind ζ-function) to obtain one of the most beautiful results of the nineteenth-century number theory: explicit formulas for the real and the relative class numbers of a cyclotomic field. We develop only the very minimum of the ζ- and L-functions theory; in particular, we do not use complex variables. As in the previous chapter, we study in detail only the prime case.

Keywords: Relative Class Number; Real Cyclotomic Field; Primary Cases; Dirichlet Character; Primitive Character (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-10094-4_5

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DOI: 10.1007/978-3-319-10094-4_5

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