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Arithmetic of non-principal orders in algebraic number fields

Andreas Philipp (2010)

Actes des rencontres du CIRM

Let R be an order in an algebraic number field. If R is a principal order, then many explicit results on its arithmetic are available. Among others, R is half-factorial if and only if the class group of R has at most two elements. Much less is known for non-principal orders. Using a new semigroup theoretical approach, we study half-factoriality and further arithmetical properties for non-principal orders in algebraic number fields.

Arithmetic of the modular function j 1 , 4

Chang Heon Kim, Ja Kyung Koo (1998)

Acta Arithmetica

We find a generator j 1 , 4 of the function field on the modular curve X₁(4) by means of classical theta functions θ₂ and θ₃, and estimate the normalized generator N ( j 1 , 4 ) which becomes the Thompson series of type 4C. With these modular functions we investigate some number theoretic properties.

Arithmetic Properties of Generalized Rikuna Polynomials

Z. Chonoles, J. Cullinan, H. Hausman, A.M. Pacelli, S. Pegado, F. Wei (2014)

Publications mathématiques de Besançon

Fix an integer ℓ ≥ 3 . Rikuna introduced a polynomial r ( x , t ) defined over a function field K ( t ) whose Galois group is cyclic of order ℓ , where K satisfies some mild hypotheses. In this paper we define the family of generalized Rikuna polynomials { r n ( x , t ) } n ≥ 1 of degree ℓ n . The r n ( x , t ) are constructed iteratively from the r ( x , t ) . We compute the Galois groups of the r n ( x , t ) for odd ℓ over an arbitrary base field and give applications to arithmetic dynamical systems.

Arithmetics in numeration systems with negative quadratic base

Zuzana Masáková, Tomáš Vávra (2011)

Kybernetika

We consider positional numeration system with negative base - β , as introduced by Ito and Sadahiro. In particular, we focus on arithmetical properties of such systems when β is a quadratic Pisot number. We study a class of roots β > 1 of polynomials x 2 - m x - n , m ≥ n ≥ 1 , and show that in this case the set Fin ( - β ) of finite ( - β ) -expansions is closed under addition, although it is not closed under subtraction. A particular example is β = τ = 1 2 ( 1 + 5 ) , the golden ratio. For such β , we determine the exact bound on the number of fractional digits...

Arithmétique d'une extension galoisienne à groupe d'inertie cyclique

Anne-Marie Bergé (1978)

Annales de l'institut Fourier

L’anneau des entiers d’une extension galoisienne de Q peut ne pas être localement libre sur son ordre associé dans l’algèbre du groupe : c’est le résultat principal de l’étude de la structure galoisienne des extensions sauvagement ramifiées d’un corps local absolument non ramifié, dans le cas où le groupe d’inertie est cyclique.

Currently displaying 341 – 360 of 3426