On quantitative aspects of the unit sum number problem

Fuchs, Clemens; Tichy, Robert F.; Ziegler, Volker

doi:10.1007/s00013-009-0037-0

Cited by 6 publications

(12 citation statements)

References 15 publications

(19 reference statements)

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“…A similar question has been investigated by Filipin, Fuchs, Tichy, and Ziegler [11,12,16]. We state here the most general result [16].…”

Section: The Quantitative Problemsupporting

confidence: 55%

Additive unit representations in rings over global fields -- A survey

Barroero¹,

Frei²,

Tichy³

2011

Publ. Math. Debrecen

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We give an overview on recent results concerning additive unit representations. Furthermore the solutions of some open questions are included. The central problem is whether and how certain rings are (additively) generated by their units. This has been investigated for several types of rings related to global fields, most importantly rings of algebraic integers. We also state some open problems and conjectures which we consider to be important in this field.

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“…A similar question has been investigated by Filipin, Fuchs, Tichy, and Ziegler [11,12,16]. We state here the most general result [16].…”

Section: The Quantitative Problemsupporting

confidence: 55%

Additive unit representations in rings over global fields -- A survey

Barroero¹,

Frei²,

Tichy³

2011

Publ. Math. Debrecen

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“…In the number field case, quantitative problems in relation with sums of units have been objects of recent study. The question, how many nonassociated algebraic integers with bounded norm in a number field can be written as a sum of exactly k units, has been investigated in [5], [6] and [7]. Similar considerations in the function field case would be of interest.…”

Section: Introductionmentioning

confidence: 99%

Sums of units in function fields

Frei

2010

Monatsh Math

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“…• 22 Actually, there was a mistake in a result that was used in [97] (this is contained in [88, Lemma 2]); this gap was successfully closed by Frei, Tichy and Ziegler.…”

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confidence: 99%

30 years of collaboration

Fuchs

Hajdu

2016

Period Math Hung

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Abstract. We highlight some of the most important cornerstones of the long standing and very fruitful collaboration of the Austrian Diophantine Number Theory research group and the Number Theory and Cryptography School of Debrecen. However, we do not plan to be complete in any sense but give some interesting data and selected results that we find particularly nice. At the end we focus on two topics in more details, namely a problem that origins from a conjecture of Rényi and Erdős (on the number of terms of the square of a polynomial) and another one that origins from a question of Zelinsky (on the unit sum number problem), which will be presented in turn.

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On quantitative aspects of the unit sum number problem

Abstract: Abstract. We investigate the function u K,S (m; q), which counts the number of representations of algebraic integers α with |N K/Q (α)| ≤ q, so that they can be written as sum of exactly m S-units of the number field K.

Cited by 6 publications

References 15 publications

Additive unit representations in rings over global fields -- A survey

Additive unit representations in rings over global fields -- A survey

Sums of units in function fields

30 years of collaboration

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