# Sums of units in function fields

@article{Frei2011SumsOU, title={Sums of units in function fields}, author={Christopher Frei}, journal={Monatshefte f{\"u}r Mathematik}, year={2011}, volume={164}, pages={39-54} }

Let R be the ring of S-integers of an algebraic function field (in one variable) over a perfect field, where S is finite and not empty. It is shown that for every positive integer N there exist elements of R that can not be written as a sum of at most N units. Moreover, all quadratic global function fields whose rings of integers are generated by their units are determined.

## 8 Citations

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We give an affirmative answer to the following question by Jarden and Narkiewicz: Is it true that every number field has a finite extension L such that the ring of integers of L is generated by its…

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We give an overview on recent results concerning additive unit representations. Furthermore the solutions of some open questions are in- cluded. The central problem is whether and how certain rings…

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We give an overview on recent results concerning additive unit representations. Furthermore the solutions of some open questions are included. We focus on rings of integers in number fields and in…

On the sumsets of exceptional units in $$\mathbb {Z}_n$$Zn

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Let R be a commutative ring with $$1\in R$$1∈R and $$R^{*}$$R∗ be the multiplicative group of its units. In 1969, Nagell introduced the concept of an exceptional unit, namely a unit u such that…

30 years of collaboration

- Mathematics, Computer SciencePeriod. Math. Hung.
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This paper focuses on two topics in more detail, 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 originated from a question of Zelinsky ( on the unit sum number problem).

Representaion of Algebraic Integers as Sum of Units over the Real Quadratic Fields

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- 2020

في هذا البحث تم تعميم نتائج الباحث جاكوبسن بأستخدام الوحدات الأساسية للحقل التربيعي الحقيقي ممثلة في الشرطين التاليين:
عندما , والشرط الثاني هو
, وبأستخدام هذه الشروط أستطعنا أثبات أن الحقل…

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