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1 June 2007 On the minimum norm of representatives of residue classes in number fields
Jean Bourgain, Mei-Chu Chang
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Duke Math. J. 138(2): 263-280 (1 June 2007). DOI: 10.1215/S0012-7094-07-13824-9

Abstract

In this article, we consider the problem of finding upper bounds on the minimum norm of representatives in residue classes in quotient O/I, where I is an integral ideal in the maximal order O of a number field K. In particular, we answer affirmatively a question of Konyagin and Shparlinski [KS], stating that an upper bound o(N(I)) holds for most ideals I, denoting N(I) the norm of I. More precise statements are obtained, especially when I is prime. We use the method of exponential sums over multiplicative groups, essentially exploiting some new bounds obtained by the authors

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Jean Bourgain. Mei-Chu Chang. "On the minimum norm of representatives of residue classes in number fields." Duke Math. J. 138 (2) 263 - 280, 1 June 2007. https://doi.org/10.1215/S0012-7094-07-13824-9

Information

Published: 1 June 2007
First available in Project Euclid: 5 June 2007

zbMATH: 1139.11035
MathSciNet: MR2318285
Digital Object Identifier: 10.1215/S0012-7094-07-13824-9

Subjects:
Primary: 11L051 , 11R27
Secondary: 11L07 , 11R04

Rights: Copyright © 2007 Duke University Press

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Vol.138 • No. 2 • 1 June 2007
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