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Volume as a Measure of Approximation for the Jacobi–Perron Algorithm
Published/Copyright:
March 19, 2010
Abstract
We consider the values of the consecutive minima of the quantities 
. W. Schmidt, in 1958, calculated the first and second minimum for j = 1 and d = 2. Schweiger, in 1975, considered the case j = 1 for any d ≥ 2. This note is a continuation of these investigations.
Received: 2008-11-07
Accepted: 2009-11-24
Published Online: 2010-03-19
Published in Print: 2010-March
© de Gruyter 2010
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Articles in the same Issue
- Congruences for Hyper m-ary Overpartition Functions
- A Note on Fibonacci-Type Polynomials
- Non-Regularity of ⌊α + logk n⌋
- Lerch's Theorems over Function Fields
- On Normal Numbers and Powers of Algebraic Numbers
- Volume as a Measure of Approximation for the Jacobi–Perron Algorithm
- Combinatorics of Integer Partitions in Arithmetic Progression
- Analogues of Jacobi's Two-Square Theorem: An Informal Account
- Convolution Identities for Stirling Numbers of the First Kind
- Pattern Occurrence in the Dyadic Expansion of Square Root of Two and an Analysis of Pseudorandom Number Generators
- Place-Difference-Value Patterns: A Generalization of Generalized Permutation and Word Patterns
- A Multivariate Arithmetic Function of Combinatorial and Topological Significance
