Representing algebraic integers as linear combinations of units

D. Dombek, L. Hajdu, A. Pethő

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper we consider representations of algebraic integers of a number field as linear combinations of units with coefficients coming from a fixed small set, and as sums of elements having small norms in absolute value. These theorems can be viewed as results concerning a generalization of the so-called unit sum number problem, as well. Beside these, extending previous related results we give an upper bound for the length of arithmetic progressions of t-term sums of algebraic integers having small norms in absolute value.

Original languageEnglish
Pages (from-to)135-142
Number of pages8
JournalPeriodica Mathematica Hungarica
Volume68
Issue number2
DOIs
Publication statusPublished - 2014

Fingerprint

Algebraic integer
Linear Combination
Absolute value
Unit
Norm
Arithmetic sequence
Number field
Upper bound
Coefficient
Term
Theorem

Keywords

  • Arithmetic progressions
  • Elements of given norm
  • Linear combinations of units

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Representing algebraic integers as linear combinations of units. / Dombek, D.; Hajdu, L.; Pethő, A.

In: Periodica Mathematica Hungarica, Vol. 68, No. 2, 2014, p. 135-142.

Research output: Contribution to journalArticle

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