Sums of two squares in short intervals
<i>Analytic Number Theory: In Honor of Helmut Maier’s 60th Birthday.</i> <br/>We show that there are short intervals [x, x + y] containing ≫ y 1∕10 numbers expressible as the sum of two squares, which is many more than the average when y=o((logx)5/9)y=o((logx)5/9). We obtain simil...
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| Format: | Book section |
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Springer International Publishing
2015
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| _version_ | 1826281881816006656 |
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| author | Maynard, J |
| author_facet | Maynard, J |
| author_sort | Maynard, J |
| collection | OXFORD |
| description | <i>Analytic Number Theory: In Honor of Helmut Maier’s 60th Birthday.</i> <br/>We show that there are short intervals [x, x + y] containing ≫ y 1∕10 numbers expressible as the sum of two squares, which is many more than the average when y=o((logx)5/9)y=o((logx)5/9). We obtain similar results for sums of two squares in short arithmetic progressions. |
| first_indexed | 2024-03-07T00:35:29Z |
| format | Book section |
| id | oxford-uuid:813f64d8-9498-4e1c-95a9-337254182bca |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:35:29Z |
| publishDate | 2015 |
| publisher | Springer International Publishing |
| record_format | dspace |
| spelling | oxford-uuid:813f64d8-9498-4e1c-95a9-337254182bca2022-03-26T21:29:06ZSums of two squares in short intervalsBook sectionhttp://purl.org/coar/resource_type/c_3248uuid:813f64d8-9498-4e1c-95a9-337254182bcaSymplectic Elements at OxfordSpringer International Publishing2015Maynard, J<i>Analytic Number Theory: In Honor of Helmut Maier’s 60th Birthday.</i> <br/>We show that there are short intervals [x, x + y] containing ≫ y 1∕10 numbers expressible as the sum of two squares, which is many more than the average when y=o((logx)5/9)y=o((logx)5/9). We obtain similar results for sums of two squares in short arithmetic progressions. |
| spellingShingle | Maynard, J Sums of two squares in short intervals |
| title | Sums of two squares in short intervals |
| title_full | Sums of two squares in short intervals |
| title_fullStr | Sums of two squares in short intervals |
| title_full_unstemmed | Sums of two squares in short intervals |
| title_short | Sums of two squares in short intervals |
| title_sort | sums of two squares in short intervals |
| work_keys_str_mv | AT maynardj sumsoftwosquaresinshortintervals |