Regular Cyclotomic Fields

David Hilbert

Chapter 31 in The Theory of Algebraic Number Fields, 1998, pp 257-268 from Springer

Abstract: Abstract Let l be an odd prime number and k (ζ) the cyclotomic field generated by = ζ = e 2πi/l is called a regular cyclotomic field and l is called a regular prime number if the number of ideal classes of the field k (ζ) is not divisible by l. The remaining chapters will be concerned exclusively with regular cyclotomic fields and with Kummer fields derived from them. Such Kummer fields will be called regular Kummer fields. We can prove at once the following simple result.

Date: 1998
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DOI: 10.1007/978-3-662-03545-0_31

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