The Paley graph conjecture and Diophantine m-tuples
| buir.contributor.author | Güloğlu, Ahmet M. | |
| buir.contributor.author | Murty, M. R. | |
| dc.citation.epage | 105155-1 | en_US |
| dc.citation.spage | 105155-9 | en_US |
| dc.citation.volumeNumber | 170 | en_US |
| dc.contributor.author | Güloğlu, Ahmet M. | |
| dc.contributor.author | Murty, M. R. | |
| dc.date.accessioned | 2021-02-24T12:25:33Z | |
| dc.date.available | 2021-02-24T12:25:33Z | |
| dc.date.issued | 2020 | |
| dc.department | Department of Mathematics | en_US |
| dc.description.abstract | A Diophantine m-tuple with property D(n), where n is a nonzero integer, is a set of m positive integers {a1, ..., am} such that aiaj + n is a perfect square for all 1 i < j m. It is known that Mn = sup{|S| : S is a D(n) m-tuple} exists and is O(log |n|). In this paper, we show that the Paley graph conjecture implies that the upper bound can be improved to (log |n|), for any > 0. | en_US |
| dc.description.provenance | Submitted by Onur Emek (onur.emek@bilkent.edu.tr) on 2021-02-24T12:25:33Z No. of bitstreams: 1 The_Paley_graph_conjecture_and_Diophantine_m-tuples.pdf: 307316 bytes, checksum: d12a905da7411c9827356360c6cacb59 (MD5) | en |
| dc.description.provenance | Made available in DSpace on 2021-02-24T12:25:33Z (GMT). No. of bitstreams: 1 The_Paley_graph_conjecture_and_Diophantine_m-tuples.pdf: 307316 bytes, checksum: d12a905da7411c9827356360c6cacb59 (MD5) Previous issue date: 2020 | en |
| dc.embargo.release | 2022-02-01 | |
| dc.identifier.doi | 10.1016/j.jcta.2019.105155 | en_US |
| dc.identifier.issn | 0097-3165 | |
| dc.identifier.uri | http://hdl.handle.net/11693/75560 | |
| dc.language.iso | English | en_US |
| dc.publisher | Elsevier | en_US |
| dc.relation.isversionof | https://dx.doi.org/10.1016/j.jcta.2019.105155 | en_US |
| dc.source.title | Journal of Combinatorial Theory, Series A | en_US |
| dc.subject | Diophantine m-tuples | en_US |
| dc.subject | Gallagher's sieve | en_US |
| dc.subject | Vinogradov's inequality | en_US |
| dc.subject | Paley graph conjecture | en_US |
| dc.title | The Paley graph conjecture and Diophantine m-tuples | en_US |
| dc.type | Article | en_US |
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