منابع مشابه
Pair Correlation Densities of Inhomogeneous Quadratic Forms
Under explicit diophantine conditions on (α, β) ∈ R2, we prove that the local two-point correlations of the sequence given by the values (m − α)2 + (n−β)2, with (m,n) ∈ Z2, are those of a Poisson process. This partly confirms a conjecture of Berry and Tabor [2] on spectral statistics of quantized integrable systems, and also establishes a particular case of the quantitative version of the Oppen...
متن کاملPerfect Delaunay Polytopes and Perfect Inhomogeneous Forms
A lattice Delaunay polytope D is called perfect if it has the property that there is a unique circumscribing ellipsoid with interior free of lattice points, and with the surface containing only those lattice points that are the vertices of D. An inhomogeneous quadratic form is called perfect if it is determined by such a circumscribing ”empty ellipsoid” uniquely up to a scale factorComplete pro...
متن کاملOn extreme forms in dimension 8
A theorem of Voronoi asserts that a lattice is extreme if and only if it is perfect and eutactic. Very recently the classification of the perfect forms in dimension 8 has been completed [5]. There are 10916 perfect lattices. Using methods of linear programming, we are able to identify those that are additionally eutactic. In lower dimensions almost all perfect lattices are also eutactic (for ex...
متن کاملExtreme Forms of Child Labour in Turkey
Two little known forms of child labour in Turkey are examined. The process through which these children are made to work has parallels with the experiences of slaves. First, a longstanding practice from Northwestern Turkey of parents hiring children to better-off farmers is examined. Further, a more recent problem is examined where children are trafficked to big cities and forced to join crimin...
متن کاملCorrection to “pair Correlation Densities of Inhomogeneous Quadratic Forms, Ii”
Proof One follows the argument in [1, pp. 432 – 433] (cf. also [2, Sec. 9]) to show that for each fixed badly approximable (k − 2)-tuple (α1, . . . , αk−2) there is a set of second Baire category of (αk−1, αk) ∈ T2 such that conditions (i), (ii), and (iii) of Theorem 1.7 hold for α = (α1, . . . , αk). Because the set of badly approximable (k − 2)-tuples is dense in Tk−2, and the set of second B...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2012
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.2748