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The Kloosterman problem for binary Hermitian lattices

The Kloosterman problem for binary Hermitian lattices A Hermitian lattice over an imaginary quadratic field $$\mathbb {Q}(\sqrt{-m})$$ Q ( - m ) is called almost universal if it represents all but finitely many positive integers. We investigate almost universal binary Hermitian lattices and provide a Bochnak-Oh type criterion on almost universality. In particular, all almost universal $$p$$ p -anisotropic binary Hermitian lattices are universal, and we give the complete list of all such Hermitian lattices. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Springer Journals

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References (23)

Publisher
Springer Journals
Copyright
Copyright © 2013 by Mathematisches Seminar der Universität Hamburg and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Algebra; Differential Geometry; Combinatorics; Number Theory; Topology; Geometry
ISSN
0025-5858
eISSN
1865-8784
DOI
10.1007/s12188-013-0088-9
Publisher site
See Article on Publisher Site

Abstract

A Hermitian lattice over an imaginary quadratic field $$\mathbb {Q}(\sqrt{-m})$$ Q ( - m ) is called almost universal if it represents all but finitely many positive integers. We investigate almost universal binary Hermitian lattices and provide a Bochnak-Oh type criterion on almost universality. In particular, all almost universal $$p$$ p -anisotropic binary Hermitian lattices are universal, and we give the complete list of all such Hermitian lattices.

Journal

Abhandlungen aus dem Mathematischen Seminar der Universität HamburgSpringer Journals

Published: Jan 1, 2014

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