 

Vítězslav Kala and
Pavlo Yatsyna
Sums of squares in Sintegers
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Published: 
October 5, 2020. 
Keywords: 
number field, totally real, Sintegers, sum of squares, Pythagoras number. 
Subject: 
11E25,11E12,11R11. 


Abstract
In totally real number fields, we characterize the rings of Sintegers (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?


Acknowledgements
The authors were supported by projects PRIMUS/20/SCI/002 (V.K., P.Y.) and UNCE/SCI/022 (V.K.) from Charles University.


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

