# Simon Kristensen

## An inhomogeneous wave equation and non-linear Diophantine approximation

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

### Standard

An inhomogeneous wave equation and non-linear Diophantine approximation. / Beresnevich, V.; Dodson, M. M.; Kristensen, S.; Levesley, J.

In: Advances in Mathematics, Vol. 217, No. 2, 2008, p. 740-760.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

### Harvard

Beresnevich, V, Dodson, MM, Kristensen, S & Levesley, J 2008, 'An inhomogeneous wave equation and non-linear Diophantine approximation' Advances in Mathematics, vol. 217, no. 2, pp. 740-760. DOI: 10.1016/j.aim.2007.09.003

### CBE

Beresnevich V, Dodson MM, Kristensen S, Levesley J. 2008. An inhomogeneous wave equation and non-linear Diophantine approximation. Advances in Mathematics. 217(2):740-760. Available from: 10.1016/j.aim.2007.09.003

### MLA

Beresnevich, V. et al."An inhomogeneous wave equation and non-linear Diophantine approximation". Advances in Mathematics. 2008, 217(2). 740-760. Available: 10.1016/j.aim.2007.09.003

### Vancouver

Beresnevich V, Dodson MM, Kristensen S, Levesley J. An inhomogeneous wave equation and non-linear Diophantine approximation. Advances in Mathematics. 2008;217(2):740-760. Available from, DOI: 10.1016/j.aim.2007.09.003

### Author

Beresnevich, V. ; Dodson, M. M. ; Kristensen, S. ; Levesley, J./ An inhomogeneous wave equation and non-linear Diophantine approximation. In: Advances in Mathematics. 2008 ; Vol. 217, No. 2. pp. 740-760

### Bibtex

@article{cbfc6450c5cf11dc8df0000ea68e967b,
title = "An inhomogeneous wave equation and non-linear Diophantine approximation",
abstract = "A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution is studied. Both the Lebesgue and Hausdorff measures of this set are obtained.",
author = "V. Beresnevich and Dodson, {M. M.} and S. Kristensen and J. Levesley",
year = "2008",
doi = "10.1016/j.aim.2007.09.003",
language = "English",
volume = "217",
pages = "740--760",
issn = "0001-8708",
publisher = "ACADEMIC PRESS INC ELSEVIER SCIENCE",
number = "2",

}

### RIS

TY - JOUR

T1 - An inhomogeneous wave equation and non-linear Diophantine approximation

AU - Beresnevich,V.

AU - Dodson,M. M.

AU - Kristensen,S.

AU - Levesley,J.

PY - 2008

Y1 - 2008

N2 - A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution is studied. Both the Lebesgue and Hausdorff measures of this set are obtained.

AB - A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution is studied. Both the Lebesgue and Hausdorff measures of this set are obtained.

U2 - 10.1016/j.aim.2007.09.003

DO - 10.1016/j.aim.2007.09.003

M3 - Journal article

VL - 217

SP - 740

EP - 760