Several types of algebraic numbers on the unit circle
β Scribed by G. Kuba
- Publisher
- Springer
- Year
- 2005
- Tongue
- English
- Weight
- 142 KB
- Volume
- 85
- Category
- Article
- ISSN
- 0003-889X
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## Abstract We consider elements __x__ + __y__$ \sqrt {-m} $ in the imaginary quadratic number field β($ \sqrt {-m} $) such that the norm __x__^2^ + __my__^2^ = 1 and both __x__ and __y__ have a finite __b__βadic expansion for an arbitrary but fixed integer base __b__. For __m__ = 2, 3, 7 and 11 a
Let \(K\) be an algebraic number field and \(k\) be a proper subfield of \(K\). Then we have the relations between the relative degree \([K: k]\) and the increase of the rank of the unit groups. Especially, in the case of \(m\) th cyclotomic field \(Q\left(\zeta_{m}\right)\), we determine the number
We study the asymptotic behavior of the sequence of polynomials orthogonal with respect to the discrete Sobolev inner product on the unit circle is a M\_M positive definite matrix or a positive semidefinite diagonal block matrix, M=l 1 + } } } +l m +m, d+ belongs to a certain class of measures, and