A problem in non-linear Diophantine approximation

TY - JOUR

T1 - A problem in non-linear Diophantine approximation

AU - Harrap, Stephen

AU - Hussain, Mumtaz

AU - Kristensen, Simon

PY - 2018/3/27

Y1 - 2018/3/27

N2 - In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is associated with a class of linear inhomogeneous partial differential equations whose solubility depends on a certain Diophantine condition. The failure of the Diophantine condition guarantees the existence of a smooth solution.

AB - In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is associated with a class of linear inhomogeneous partial differential equations whose solubility depends on a certain Diophantine condition. The failure of the Diophantine condition guarantees the existence of a smooth solution.

KW - Hausdorff dimension

KW - Hausdorff measure

KW - Khintchine-Groshev theorem

KW - non-linear Diophantine approximation

KW - partial differential equations

UR - http://www.scopus.com/inward/record.url?scp=85045661029&partnerID=8YFLogxK

U2 - 10.1088/1361-6544/aaa498

DO - 10.1088/1361-6544/aaa498

M3 - Journal article

AN - SCOPUS:85045661029

SN - 0951-7715

VL - 31

SP - 1734

EP - 1756

JO - Nonlinearity

JF - Nonlinearity

IS - 5

ER -