Arithmetic properties of series of reciprocals of algebraic integers

S. B. Andersen; S. Kristensen

doi:10.1007/s00605-019-01326-1

Arithmetic properties of series of reciprocals of algebraic integers

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

3 Citations (Scopus)

Abstract

We obtain results bounding the degree of the series ∑n=1∞1/αn, where { α_n} is a sequence of algebraic integers satisfying certain algebraic conditions and growth conditions. Our results extend results of Erdős, Hančl and Nair.

Original language	English
Journal	Monatshefte fur Mathematik
Volume	190
Issue	4
Pages (from-to)	641-656
Number of pages	16
ISSN	0026-9255
DOIs	https://doi.org/10.1007/s00605-019-01326-1
Publication status	Published - Dec 2019

Keywords

Algebraic integers
Infinite series
Irrationality
ZETA-FUNCTION
VALUES

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10.1007/s00605-019-01326-1

https://arxiv.org/pdf/1807.04515.pdf

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title = "Arithmetic properties of series of reciprocals of algebraic integers",

abstract = "We obtain results bounding the degree of the series ∑n=1∞1/αn, where { αn} is a sequence of algebraic integers satisfying certain algebraic conditions and growth conditions. Our results extend results of Erd{\H o}s, Han{\v c}l and Nair.",

keywords = "Algebraic integers, Infinite series, Irrationality, ZETA-FUNCTION, VALUES",

author = "Andersen, {S. B.} and S. Kristensen",

year = "2019",

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T1 - Arithmetic properties of series of reciprocals of algebraic integers

AU - Andersen, S. B.

AU - Kristensen, S.

PY - 2019/12

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N2 - We obtain results bounding the degree of the series ∑n=1∞1/αn, where { αn} is a sequence of algebraic integers satisfying certain algebraic conditions and growth conditions. Our results extend results of Erdős, Hančl and Nair.

AB - We obtain results bounding the degree of the series ∑n=1∞1/αn, where { αn} is a sequence of algebraic integers satisfying certain algebraic conditions and growth conditions. Our results extend results of Erdős, Hančl and Nair.

KW - Algebraic integers

KW - Infinite series

KW - Irrationality

KW - ZETA-FUNCTION

KW - VALUES

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U2 - 10.1007/s00605-019-01326-1

DO - 10.1007/s00605-019-01326-1

M3 - Journal article

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EP - 656

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

IS - 4

ER -

Arithmetic properties of series of reciprocals of algebraic integers

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Keywords

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