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Kuznecov Sum Formulae and Szeg Limit Formulae on Manifolds

โœ Scribed by Steven, Zelditch


Book ID
127206649
Publisher
Taylor and Francis Group
Year
1992
Tongue
English
Weight
984 KB
Volume
17
Category
Article
ISSN
0360-5302

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Let (r), r=1, 2, ... be a positive decreasing sequence such that r=1 (r) k diverges. Using a powerful variance argument due to Schmidt, an asymptotic formula is obtained for the number of integer solutions q of the system of Diophantine inequalities max[&qx i &: which holds for almost all points (x

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In this paper, computation of the so-called Szegรถ quadrature formulas is considered for some special weight functions on the unit circle. The case of the Lebesgue measure is more deeply analyzed. Illustrative numerical examples are also given.