scholarly journals Perfect colourings of cyclotomic integers

2012 ◽  
Vol 162 (1) ◽  
pp. 271-282 ◽  
Author(s):  
E. P. Bugarin ◽  
M. L. A. N. de las Peñas ◽  
D. Frettlöh
Keyword(s):  
Cyclotomic Integers

J ‐fields generated by roots of cyclotomic integers

Mathematika ◽  
1978 ◽  
Vol 25 (2) ◽  
pp. 242-250
Author(s):  
Veikko Ennola
Keyword(s):  
Cyclotomic Integers

scholarly journals Power Reciprocity for Binomial Cyclotomic Integers

1998 ◽  
Vol 71 (2) ◽  
pp. 245-256
Author(s):  
Charles Helou
Keyword(s):  
Cyclotomic Integers

Cyclotomic approximation lattices

2015 ◽  
Vol 11 (02) ◽  
pp. 557-567
Author(s):  
Antonino Leonardis
Keyword(s):  
Continued Fractions ◽  
The Third ◽  
Lagrange's Theorem ◽  
Cyclotomic Integers

In this paper, we will consider the Approximation Lattices for a p-adic number, as defined in a work of de Weger, and construct a generalization called the Cyclotomic Approximation Lattices. In the latter case, we consider approximation by a pair of cyclotomic integers instead of rational ones. This can be useful for studying p-adic continued fractions with cyclotomic integral part. The first section will introduce this work and provide motivations. The second one will give some background theorems on number rings. In the third section, we will recall the work of de Weger with a new proof for Theorem 3.6, the analogue of classical Lagrange's theorem for continued fractions. In the fourth one, we will then see the cyclotomic variant and its analogous properties.

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