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On Smooth Ideals in Number Fields

✍ Scribed by Johannes A Buchmann; Christine S Hollinger

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
310 KB
Volume
59
Category
Article
ISSN
0022-314X

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✦ Synopsis

For y # R >0 an integral ideal of an algebraic number field F is called y-smooth if the norms of all of its prime ideal factors are bounded by y. Assuming the generalized Riemann hypothesis we prove a lower bound for the number F (x, y) of integral y-smooth ideals in F whose norms are bounded by x # R >0 . Apart from x and y this bound only depends on the degree of F.

1996 Academic Press, Inc.

where u=log xΓ‚log y and n~is the degree of the normal closure of F over Q.

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