### 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 language | English |
---|---|

Pages (from-to) | 135-142 |

Number of pages | 8 |

Journal | Periodica Mathematica Hungarica |

Volume | 68 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Periodica Mathematica Hungarica*,

*68*(2), 135-142. https://doi.org/10.1007/s10998-014-0020-9

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

Research output: Contribution to journal › Article

*Periodica Mathematica Hungarica*, vol. 68, no. 2, pp. 135-142. https://doi.org/10.1007/s10998-014-0020-9

}

TY - JOUR

T1 - Representing algebraic integers as linear combinations of units

AU - Dombek, D.

AU - Hajdu, L.

AU - Pethő, A.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Arithmetic progressions

KW - Elements of given norm

KW - Linear combinations of units

UR - http://www.scopus.com/inward/record.url?scp=84902358942&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902358942&partnerID=8YFLogxK

U2 - 10.1007/s10998-014-0020-9

DO - 10.1007/s10998-014-0020-9

M3 - Article

AN - SCOPUS:84902358942

VL - 68

SP - 135

EP - 142

JO - Periodica Mathematica Hungarica

JF - Periodica Mathematica Hungarica

SN - 0031-5303

IS - 2

ER -