Pythagoras numbers for infinite algebraic fields

Revista Matemática Complutense 2026 Open access

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Authors: Nicolas Daans, Stevan Gajović, Siu Hang Man, Pavlo Yatsyna
DOI: 10.1007/s13163-026-00562-y
Cited by: 0
References: 19

Abstract

Abstract We prove that the Pythagoras number of the ring of integers of the compositum of all real quadratic fields is infinite. The same holds for certain infinite totally real cyclotomic fields. In contrast, we construct infinite degree totally real algebraic fields whose rings of integers have finite Pythagoras numbers, namely, one, two, three, and at least four.

Fields of Study & Subjects

Mathematical and Theoretical Analysis History and Theory of Mathematics Rings Modules and Algebras

Publication details

Journal / source
Revista Matemática Complutense
Publisher
Springer Science and Business Media LLC
Publication date
31 January 2026
Language
EN