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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
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### 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",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press",

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

JO - Advances in Mathematics

T2 - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 2

ER -