Sums of squares of integer-multiple of an integral element on real bi-quadratic fields

2021/12/29 by Srijonee Shabnam Chaudhury, Chaudhury, Srijonee Shabnam
Mathematics · #11E25 #11R16 #11R33 #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2112.14489

openalex publication_date 2021/12/29 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

For any given positive integer m we construct certain totally positive algebraic integers α of a real bi-quadratic field K and obtain some necessary conditions for which mα can not be represented as sum of integral squares. We show this for integers lie in quadratic subfields of K and for integers which are in K but not in any quadratic subfield of K. We provide examples in tabular form for each cases to corroborate the results.

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