Bounds for the cubic Weyl sum
Subject to the abc-conjecture, we improve the standard Weyl estimate for cubic exponential sums in which the argument is a quadratic irrational. Specifically. we show that, for any ε > 0 and any quadratic irrational α ∈ ℝ-ℚ. Classically one would have had the (unconditional) exponent 3/4 + ε...
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| Materyal Türü: | Journal article |
| Dil: | English |
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2010
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| _version_ | 1826288799735349248 |
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| author | Heath-Brown, DR |
| author_facet | Heath-Brown, DR |
| author_sort | Heath-Brown, DR |
| collection | OXFORD |
| description | Subject to the abc-conjecture, we improve the standard Weyl estimate for cubic exponential sums in which the argument is a quadratic irrational. Specifically. we show that, for any ε > 0 and any quadratic irrational α ∈ ℝ-ℚ. Classically one would have had the (unconditional) exponent 3/4 + ε for such α. Bibliography: 5 titles. © 2010 Springer Science+Business Media, Inc. |
| first_indexed | 2024-03-07T02:19:10Z |
| format | Journal article |
| id | oxford-uuid:a34e44e8-4149-4a1c-9a76-3396c31c7ca8 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:19:10Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:a34e44e8-4149-4a1c-9a76-3396c31c7ca82022-03-27T02:26:03ZBounds for the cubic Weyl sumJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a34e44e8-4149-4a1c-9a76-3396c31c7ca8EnglishSymplectic Elements at Oxford2010Heath-Brown, DRSubject to the abc-conjecture, we improve the standard Weyl estimate for cubic exponential sums in which the argument is a quadratic irrational. Specifically. we show that, for any ε > 0 and any quadratic irrational α ∈ ℝ-ℚ. Classically one would have had the (unconditional) exponent 3/4 + ε for such α. Bibliography: 5 titles. © 2010 Springer Science+Business Media, Inc. |
| spellingShingle | Heath-Brown, DR Bounds for the cubic Weyl sum |
| title | Bounds for the cubic Weyl sum |
| title_full | Bounds for the cubic Weyl sum |
| title_fullStr | Bounds for the cubic Weyl sum |
| title_full_unstemmed | Bounds for the cubic Weyl sum |
| title_short | Bounds for the cubic Weyl sum |
| title_sort | bounds for the cubic weyl sum |
| work_keys_str_mv | AT heathbrowndr boundsforthecubicweylsum |