## Abstract We prove the algebraic eigenvalue conjecture of J. Dodziuk, P. Linnell, V. Mathai, T. Schick, and S. Yates (see [2]) for sofic groups. Moreover, we give restrictions on the spectral measure of elements in the integral group ring. Finally, we define integer operators and prove a quantiza
Diophantine Approximation On Bianchi Groups
โ Scribed by L.Y. Vulakh
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 290 KB
- Volume
- 54
- Category
- Article
- ISSN
- 0022-314X
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โฆ Synopsis
A modification of the Ford geometric approach to the problem of approximation of complex numbers by elements of an imaginary quadratic number field is developed. An upper bound for the Hurwitz constant for the field is obtained in terms of the geometry of the isometric fundamental domain for the corresponding Bianchi group. The Hurwitz constants for the fields of discriminant -20 and -24 are found. 1995 Academic Press, Inc.
๐ SIMILAR VOLUMES
A new approach to inhomogeneous Diophantine approximation is given and a method for the computation of inhomogeneous minima of binary quadratic forms is derived. The new method is simpler than earlier ones of Barnes and SwinnertonDyer. As an application, a new proof of a theorem of Davenport, which