On the representations of integers by the sextenary quadratic form x2 + y2 + z2 + 7 s2 + 7 t2 + 7 u2 and 7-cores
| dc.citation.epage | 1378 | en_US |
| dc.citation.issueNumber | 6 | en_US |
| dc.citation.spage | 1366 | en_US |
| dc.citation.volumeNumber | 129 | en_US |
| dc.contributor.author | Berkovich, A. | en_US |
| dc.contributor.author | Yesilyurt H. | en_US |
| dc.date.accessioned | 2016-02-08T10:04:01Z | |
| dc.date.available | 2016-02-08T10:04:01Z | |
| dc.date.issued | 2009 | en_US |
| dc.department | Department of Mathematics | en_US |
| dc.description.abstract | In this paper we derive an explicit formula for the number of representations of an integer by the sextenary form x2 + y2 + z2 + 7 s2 + 7 t2 + 7 u2. We establish the following intriguing inequalities2 ω (n + 2) ≥ a7 (n) ≥ ω (n + 2) for n ≠ 0, 2, 6, 16 . Here a7 (n) is the number of partitions of n that are 7-cores and ω (n) is the number of representations of n by the sextenary form (x2 + y2 + z2 + 7 s2 + 7 t2 + 7 u2) / 8 with x, y, z, s, t and u being odd positive integers. © 2008 Elsevier Inc. All rights reserved. | en_US |
| dc.identifier.doi | 10.1016/j.jnt.2008.09.001 | en_US |
| dc.identifier.issn | 0022-314X | |
| dc.identifier.uri | http://hdl.handle.net/11693/22728 | |
| dc.language.iso | English | en_US |
| dc.publisher | Academic Press | en_US |
| dc.relation.isversionof | http://dx.doi.org/10.1016/j.jnt.2008.09.001 | en_US |
| dc.source.title | Journal of Number Theory | en_US |
| dc.subject | 7-cores | en_US |
| dc.subject | Modular equations | en_US |
| dc.subject | Sextenary forms | en_US |
| dc.title | On the representations of integers by the sextenary quadratic form x2 + y2 + z2 + 7 s2 + 7 t2 + 7 u2 and 7-cores | en_US |
| dc.type | Article | en_US |
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