dc.contributor.author | Pritsker, Igor E | |
dc.date.accessioned | 2024-01-17T19:51:14Z | |
dc.date.available | 2024-01-17T19:51:14Z | |
dc.date.issued | 2021-01-17 | |
dc.identifier | oksd_pritsker_house_of_algebraic_integers_2021 | |
dc.identifier.citation | Pritsker, I.E. (2021). House of algebraic integers symmetric about the unit circle. https://doi.org/10.48550/arxiv.2101.06710 | |
dc.identifier.uri | https://hdl.handle.net/11244/340123 | |
dc.description.abstract | We give a Schinzel-Zassenhaus-type lower bound for the maximum modulus of roots of a monic integer polynomial with all roots symmetric with respect to the unit circle. Our results extend a recent work of Dimitrov, who proved the general Schinzel-Zassenhaus conjecture by using the Pólya rationality theorem for a power series with integer coefficients, and some estimates for logarithmic capacity (transfinite diameter) of sets. We use an enhancement of Pólya’s result obtained by Robinson, which involves Laurent-type rational functions with small supremum norms, thereby replacing the logarithmic capacity with a smaller quantity. This smaller quantity is expressed via a weighted Chebyshev constant for the set associated with Dimitrov’s function used in Robinson’s rationality theorem. Our lower bound for the house confirms a conjecture of Boyd. | |
dc.format | application/pdf | |
dc.language | en_US | |
dc.rights | This material has been previously published. In the Oklahoma State University Library's institutional repository this version is made available through the open access principles and the terms of agreement/consent between the author(s) and the publisher. The permission policy on the use, reproduction or distribution of the material falls under fair use for educational, scholarship, and research purposes. Contact Digital Resources and Discovery Services at lib-dls@okstate.edu or 405-744-9161 for further information. | |
dc.title | House of algebraic integers symmetric about the unit circle | |
dc.date.updated | 2024-01-16T23:27:46Z | |
osu.filename | oksd_pritsker_house_of_algebraic_integers_2021.pdf | |
dc.identifier.doi | 10.48550/arxiv.2101.06710 | |
dc.description.department | Mathematics | |
dc.type.genre | Preprint | |
dc.type.material | Text | |
dc.subject.keywords | applied mathematics | |
dc.subject.keywords | numerical and computational mathematics | |
dc.subject.keywords | pure mathematics | |
dc.subject.keywords | mathematical sciences | |
dc.identifier.author | ORCID: 0000-0002-3102-5003 (Pritsker, Igor E) | |
dc.identifier.author | ScopusID: 6602900239 (Pritsker, Igor E) | |