Equal Sums of Two $k$th Powers
Let <i>k</i> ≥ 5 be an integer, and let <i>x</i> ≥ 1 be an arbitrary real number. We derive a bound <br/><br/> <i>O<sub>ε,k</sub></i> (x<sup>2/3<i>k</i>+ε</sup> + x<sup>3/<i>k</i>√<i>k</i&g...
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| Format: | Journal article |
| Language: | English |
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Elsevier
2002
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| _version_ | 1797101558314303488 |
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| author | Browning, T |
| author2 | Academic Press |
| author_facet | Academic Press Browning, T |
| author_sort | Browning, T |
| collection | OXFORD |
| description | Let <i>k</i> ≥ 5 be an integer, and let <i>x</i> ≥ 1 be an arbitrary real number. We derive a bound <br/><br/> <i>O<sub>ε,k</sub></i> (x<sup>2/3<i>k</i>+ε</sup> + x<sup>3/<i>k</i>√<i>k</i>+2/<i>k</i>(<i>k</i>-1)+ε</sup>),<br/><br/> for the number of positive integers less than or equal to x which can be represented as a sum of two non-negative coprime kth powers, in essentially more than one way. |
| first_indexed | 2024-03-07T05:53:33Z |
| format | Journal article |
| id | oxford-uuid:e9bb12fd-abae-4326-9c18-e49ecd6e6406 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:53:33Z |
| publishDate | 2002 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:e9bb12fd-abae-4326-9c18-e49ecd6e64062022-03-27T10:56:23ZEqual Sums of Two $k$th PowersJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e9bb12fd-abae-4326-9c18-e49ecd6e6406Number theoryMathematicsEnglishOxford University Research Archive - ValetElsevier2002Browning, TAcademic PressLet <i>k</i> ≥ 5 be an integer, and let <i>x</i> ≥ 1 be an arbitrary real number. We derive a bound <br/><br/> <i>O<sub>ε,k</sub></i> (x<sup>2/3<i>k</i>+ε</sup> + x<sup>3/<i>k</i>√<i>k</i>+2/<i>k</i>(<i>k</i>-1)+ε</sup>),<br/><br/> for the number of positive integers less than or equal to x which can be represented as a sum of two non-negative coprime kth powers, in essentially more than one way. |
| spellingShingle | Number theory Mathematics Browning, T Equal Sums of Two $k$th Powers |
| title | Equal Sums of Two $k$th Powers |
| title_full | Equal Sums of Two $k$th Powers |
| title_fullStr | Equal Sums of Two $k$th Powers |
| title_full_unstemmed | Equal Sums of Two $k$th Powers |
| title_short | Equal Sums of Two $k$th Powers |
| title_sort | equal sums of two k th powers |
| topic | Number theory Mathematics |
| work_keys_str_mv | AT browningt equalsumsoftwokthpowers |