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Vítězslav Kala and
Pavlo Yatsyna
Sums of squares in S-integers
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| Published: |
October 5, 2020. |
| Keywords: |
number field, totally real, S-integers, sum of squares, Pythagoras number. |
| Subject: |
11E25,11E12,11R11. |
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Abstract
In totally real number fields, we characterize the rings of S-integers (obtained by inverting a rational integer m) such that all their totally positive elements are represented as a sum of squares. We further obtain partial answers to the question: when are all the totally positive algebraic integers that are divisible by m represented as a sum of squares?
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| Acknowledgements
The authors were supported by projects PRIMUS/20/SCI/002 (V.K., P.Y.) and UNCE/SCI/022 (V.K.) from Charles University.
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| Author information
Vítězslav Kala:
Charles University
Faculty of Mathematics and Physics
Department of Algebra
Sokolovska 83, 18600 Praha 8, Czech Republic
kala@karlin.mff.cuni.cz
Pavlo Yatsyna:
Charles University
Faculty of Mathematics and Physics
Department of Algebra
Sokolovska 83, 18600 Praha 8, Czech Republic
yatsyna@karlin.mff.cuni.cz
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