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Relative norms of prime ideals in small regions

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  26 February 2010

M. D. Coleman
M. D. Coleman
Affiliation:
Department of Mathematics, UMIST, P. O. Box 88, Manchester. M60 1QD
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Extract

Let K be a number field of degree nK = r1 + 2r2, a fixed integral ideal and the group of fractional ideals of K whose prime decomposition contains no prime factors of . Let

and be an arbitrary Groessencharaktere mod f as defined in [15]. Then and, for

where {λi} forms a basis for the torsion–free characters on whose value on any depends only on the that exists such that a = (α). Note that because of the choice in such an α we have that 1 for all units ε in K satisfying (mod ), ε>0. Also, x is a narrow ideal class character mod , that is, a character on

MSC classification

Secondary: 11R44: Distribution of prime ideals
Type
Research Article
Information
Mathematika , Volume 43 , Issue 1 , June 1996 , pp. 40 - 62
Copyright
Copyright © University College London 1996

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