On minimum norm of representatives of residue classes in number fields

DOI10.1215/S0012-7094-07-13824-9zbMath1139.11035MaRDI QIDQ2371896

Mei-Chu Chang, Jean Bourgain

Publication date: 9 July 2007

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

exponential sumsnumber fieldsintegral idealsminimum norm representatives

Mathematics Subject Classification ID

Units and factorization (11R27) Estimates on exponential sums (11L07) Gauss and Kloosterman sums; generalizations (11L05) Algebraic numbers; rings of algebraic integers (11R04)

Related Items (1)

Exponential sum estimates in finite commutative rings and applications

Cites Work

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• The distribution of residue classes modulo a in an algebraic number field
• Exponential sum estimates over subgroups and almost subgroups of \(\mathbb Z_Q^*\), where \(Q\) is composite with few prime factors
• A Gauss sum estimate in arbitrary finite fields
• Multi-Invariant Sets on Tori
• Mordell’s exponential sum estimate revisited
• On the periods of the linear congruential and power generators
• ESTIMATES FOR THE NUMBER OF SUMS AND PRODUCTS AND FOR EXPONENTIAL SUMS IN FIELDS OF PRIME ORDER
• Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
• On quantum ergodicity for linear maps of the torus.

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