Sums of squares of integer-multiple of an integral element on real bi-quadratic fields
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866916118590914560 |
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| author | Chaudhury, Srijonee Shabnam |
| author_facet | Chaudhury, Srijonee Shabnam |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2112_14489 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Sums of squares of integer-multiple of an integral element on real bi-quadratic fields Chaudhury, Srijonee Shabnam Number Theory 11E25, 11R16, 11R33 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. |
| title | Sums of squares of integer-multiple of an integral element on real bi-quadratic fields |
| topic | Number Theory 11E25, 11R16, 11R33 |
| url | https://arxiv.org/abs/2112.14489 |