The representation of integers by binary additive forms
dc.contributor.author | Bennett, M. A. | en_US |
dc.contributor.author | Dummigan, N. P. | en_US |
dc.contributor.author | Wooley, Trevor D. | en_US |
dc.date.accessioned | 2006-09-08T20:30:48Z | |
dc.date.available | 2006-09-08T20:30:48Z | |
dc.date.issued | 1998-03 | en_US |
dc.identifier.citation | Bennett, M. A.; Dummigan, N. P.; Wooley, T. D.; (1998). "The representation of integers by binary additive forms." Compositio Mathematica 111(1): 15-33. <http://hdl.handle.net/2027.42/42597> | en_US |
dc.identifier.issn | 0010-437X | en_US |
dc.identifier.issn | 1570-5846 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/42597 | |
dc.description.abstract | Let a, b and n be integers with ≥ 3. We show that, in the sense of natural density, almost all integers represented by the binary form ax n − by n are thus represented essentially uniquely. By exploiting this conclusion, we derive an asymptotic formula for the total number of integers represented by such a form. These conclusions augment earlier work of Hooley concerning binary cubic and quartic forms, and generalise or sharpen work of Hooley, Greaves, and Skinner and Wooley concerning sums and differences of two nth powers. | en_US |
dc.format.extent | 182404 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Kluwer Academic Publishers; Springer Science+Business Media | en_US |
dc.subject.other | Mathematics | en_US |
dc.subject.other | Mathematics, General | en_US |
dc.subject.other | Binary Forms | en_US |
dc.subject.other | Representation Problems | en_US |
dc.subject.other | Higher Degree Equations | en_US |
dc.subject.other | Diophantine Approximation | en_US |
dc.subject.other | Waring's Problem and Variants | en_US |
dc.title | The representation of integers by binary additive forms | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Mathematics Department, University of Michigan, Ann Arbor, Michigan, 48109-1003 | en_US |
dc.contributor.affiliationum | Mathematics Department, University of Michigan, Ann Arbor, Michigan, 48109-1003; Mathematics Department, Northern Illinois University, De Kalb, Illinois, 60115-2888 | en_US |
dc.contributor.affiliationum | Mathematics Department, University of Michigan, Ann Arbor, Michigan, 48109-1003 | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/42597/1/10599_2004_Article_129125.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1023/A:1000270823971 | en_US |
dc.identifier.source | Compositio Mathematica | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
Files in this item
Remediation of Harmful Language
The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.
Accessibility
If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.