Year: 2008
Type: article
Abstract: In the p n -th cyclotomic field ℚ p n , p a prime number, n ∈ ℕ , the prime p is totally ramified and the only ideal above p is generated by ω n = ζ p n - 1 , with the primitive p n -th root of unity ζ p n = e 2 π i p n . Moreover these numbers represent a norm coherent set, i.e. N ℚ p n + 1 / ℚ p n ( ω n + 1 ) = ω n . It is the aim of this article to establish a similar result for the ray class field K 𝔭 n of conductor 𝔭 n over an imaginary quadratic number field K where 𝔭 n is the power of a prime ideal in K . Therefore the exponential function has to be replaced by a suitable elliptic function.
DOI: 10.5802/jtnb.566
Author: Reinhard Schertz
Institution: University of Augsburg
Language: Latvian
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2315777443