On inhomogeneous diophantine approximation

Thomas W. Cusick; Andrew M. Rockett; Peter Szüsz

doi:10.1006/jnth.1994.1067

On inhomogeneous diophantine approximation

Thomas W. Cusick
, Andrew M. Rockett
, Peter Szüsz

Mathematics

Long Island University
Stony Brook University

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

A new approach to inhomogeneous Diophantine approximation is given and a method for the computation of inhomogeneous minima of binary quadratic forms is derived. The new method is simpler than earlier ones of Barnes and Swinnerton-Dyer. As an application, a new proof of a theorem of Davenport, which gives the complete sequence of inhomogeneous minima for the form x² - xy - y², is given.

Original language	English
Pages (from-to)	259-283
Number of pages	25
Journal	Journal of Number Theory
Volume	48
Issue number	3
DOIs	https://doi.org/10.1006/jnth.1994.1067
State	Published - Sep 1994

Access to Document

10.1006/jnth.1994.1067

Cite this

@article{a45233c330cd4699b7984ff8f9cfb7d3,

title = "On inhomogeneous diophantine approximation",

abstract = "A new approach to inhomogeneous Diophantine approximation is given and a method for the computation of inhomogeneous minima of binary quadratic forms is derived. The new method is simpler than earlier ones of Barnes and Swinnerton-Dyer. As an application, a new proof of a theorem of Davenport, which gives the complete sequence of inhomogeneous minima for the form x2 - xy - y2, is given.",

author = "Cusick, \{Thomas W.\} and Rockett, \{Andrew M.\} and Peter Sz{\"u}sz",

year = "1994",

month = sep,

doi = "10.1006/jnth.1994.1067",

language = "English",

volume = "48",

pages = "259--283",

journal = "Journal of Number Theory",

issn = "0022-314X",

publisher = "Academic Press Inc.",

number = "3",

}

TY - JOUR

T1 - On inhomogeneous diophantine approximation

AU - Cusick, Thomas W.

AU - Rockett, Andrew M.

AU - Szüsz, Peter

PY - 1994/9

Y1 - 1994/9

N2 - A new approach to inhomogeneous Diophantine approximation is given and a method for the computation of inhomogeneous minima of binary quadratic forms is derived. The new method is simpler than earlier ones of Barnes and Swinnerton-Dyer. As an application, a new proof of a theorem of Davenport, which gives the complete sequence of inhomogeneous minima for the form x2 - xy - y2, is given.

AB - A new approach to inhomogeneous Diophantine approximation is given and a method for the computation of inhomogeneous minima of binary quadratic forms is derived. The new method is simpler than earlier ones of Barnes and Swinnerton-Dyer. As an application, a new proof of a theorem of Davenport, which gives the complete sequence of inhomogeneous minima for the form x2 - xy - y2, is given.

UR - https://www.scopus.com/pages/publications/0001214083

U2 - 10.1006/jnth.1994.1067

DO - 10.1006/jnth.1994.1067

M3 - Article

AN - SCOPUS:0001214083

SN - 0022-314X

VL - 48

SP - 259

EP - 283

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 3

ER -

On inhomogeneous diophantine approximation

Abstract

Access to Document

Other files and links

Fingerprint

Cite this