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] Deza , E. , Varukhina , L. 2008 On mean values of some arithmetic functions in number fields Discrete Math. 308 4892 – 4899 10.1016/j.disc.2007.09.008 . [4] Heath-Brown , D. R

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] L . El Fadil . Computation of a power integral basis of a pure cubic number field . Int. J. Con-temp. Math. Sci ., 2 ( 13-16 ): 601 – 606 , 2007 . [5

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Introduction Let K be a number field defined by a monic irreducible polynomial f ( x ) ∈ℤ[ x ] and ℤ K its ring of integers. It is well know that the ring ℤ K is a free ℤ-module of rank n = [ K :ℚ]. Thus the abelian group ℤ K /ℤ[α] is finite

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Abstract  

In this paper we compute the box counting dimension of sets, that are related to number systems in real quadratic number fields. The sets under discussion are so-called graph-directed self affine sets. Contrary to the case of self similar sets, for self affine sets there does not exist a general theory for the determination of the box counting dimension. Thus we are forced to construct the covers, needed for its calculation, directly.

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Abstract  

In this paper, we present several methods for the construction of elliptic curves with large torsion group and positive rank over number fields of small degree. We also discuss potential applications of such curves in the elliptic curve factorization method (ECM).

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