منابع مشابه
Applications of quadratic D-forms to generalized quadratic forms
In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.
متن کاملPair 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 کاملLocality of Quadratic Forms for Point Perturbations of Schrödinger Operators
In this paper we study point perturbations of the Schrödinger operators within the framework of Krein’s theory of self-adjoint extensions. A locality criterion for quadratic forms is proved for such perturbations.
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...
متن کاملPair Correlation Densities of Inhomogeneous Quadratic Forms Ii
Abstract. Denote by ‖ · ‖ the euclidean norm in R. We prove that the local pair correlation density of the sequence ‖m− α‖k, m ∈ Z, is that of a Poisson process, under diophantine conditions on the fixed vector α ∈ R: in dimension two, vectors α of any diophantine type are admissible; in higher dimensions (k > 2), Poisson statistics are only observed for diophantine vectors of type κ < (k − 1)/...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2015
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-015-0817-5