Journal article
The circle method and diagonal cubic forms
- Abstract:
- We use the Hardy-Littlewood circle method, in the form developed by Heath-Brown in 1996, to investigate the number of integer zeros of diagonal cubic forms. The results are subject to unproved hypotheses concerning certain Hasse-Weil L-functions. For six variables we show that there are O(P3+ε) zeros up to height P, for any ε > 0. For four variables we show that there are O(P3/2+ε) such zeros, excluding any that lie on rational lines in the corresponding surface.
- Publication status:
- Published
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- Publisher copy:
- 10.1098/rsta.1998.0181
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Authors
Bibliographic Details
- Journal:
- PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
- Volume:
- 356
- Issue:
- 1738
- Pages:
- 673-699
- Publication date:
- 1998-03-15
- DOI:
- EISSN:
-
1471-2962
- ISSN:
-
1364-503X
- URN:
-
uuid:cbb63efe-f7e8-4d01-88a8-27837fc80e83
- Source identifiers:
-
15477
- Local pid:
- pubs:15477
Item Description
- Language:
- English
- Keywords:
Terms of use
- Copyright date:
- 1998
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