Uniformly Diophantine numbers in a fixed real quadratic field

Publisher： Cambridge University Press

E-ISSN： 1570-5846|145|4|827-844

ISSN： 0010-437x

Source： Compositio Mathematica, Vol.145, Iss.4, 2009-07, pp. : 827-844

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

The field $\mathbb {Q}(\sqrt {5})$ contains the infinite sequence of uniformly bounded continued fractions $[\overline {1,4,2,3}], [\overline {1,1,4,2,1,3}], [\overline {1,1,1,4,2,1,1,3}], \ldots ,$ and similar patterns can be found in $\mathbb {Q}(\sqrt {d})$ for any d>0. This paper studies the broader structure underlying these patterns, and develops related results and conjectures for closed geodesics on arithmetic manifolds, packing constants of ideals, class numbers and heights.

Related content

Class numbers of real quadratic fields

By  

Bulletin of the Australian Mathematical Society, Vol. 57, Iss. 2, 1998-04 ,pp. : 261-274 (14)

Cambridge University Press

Access to resources Recommend Favorite

Bounds of the Ideal Class Numbers of Real Quadratic Function Fields

By Wang Kun   Zhang Xian  

Acta Mathematica Sinica, Vol. 20, Iss. 1, 2004-01 ,pp. : 169-174 (6)

Springer Publishing Company

Access to resources Recommend Favorite

COMPUTING STRENGTH OF STRUCTURES RELATED TO THE FIELD OF REAL NUMBERS

By  

The Journal of Symbolic Logic, Vol. 82, Iss. 1, 2017-03 ,pp. : 137-150 (14)

Cambridge University Press

Access to resources Recommend Favorite

A DIOPHANTINE PROBLEM CONCERNING POLYGONAL NUMBERS

By  

Bulletin of the Australian Mathematical Society, Vol. 88, Iss. 2, 2013-10 ,pp. : 345-350 (6)

Cambridge University Press

Access to resources Recommend Favorite

Use of the rabinowitsch polynomial to determine the class groups of a real quadratic field

By  

Bulletin of the Australian Mathematical Society, Vol. 50, Iss. 3, 1994-12 ,pp. : 435-443 (9)

Cambridge University Press

Access to resources Recommend Favorite