dc.contributor.author | Pritsker, Igor | |
dc.date.accessioned | 2024-01-17T19:53:06Z | |
dc.date.available | 2024-01-17T19:53:06Z | |
dc.date.issued | 2021-01-17 | |
dc.identifier | oksd_pritzker_heights_of_polynomials_over_2021 | |
dc.identifier.citation | Pritsker, I. (2021). Heights of polynomials over lemniscates. 10.48550/arXiv.2101.06708 | |
dc.identifier.uri | https://hdl.handle.net/11244/340124 | |
dc.description.abstract | We consider a family of heights defined by the Lₚ norms of polynomials with respect to the equilibrium measure of a lemniscate for 0 ≤ p ≤ ∞, where p = 0 corresponds to the geometric mean (the generalized Mahler measure) and p = ∞ corresponds to the standard supremum norm. This special choice of the measure allows to find an explicit form for the geometric mean of a polynomial, and estimate it via certain resultant. For lemniscates satisfying appropriate hypotheses, we establish explicit polynomials of lowest height, and also show their uniqueness. We discuss relations between the standard results on the Mahler measure and their analogues for lemniscates that include generalizations of Kronecker’s theorem on algebraic integers in the unit disk, as well as of Lehmer’s conjecture. | |
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 | Heights of polynomials over lemniscates | |
dc.date.updated | 2024-01-16T23:28:05Z | |
osu.filename | oksd_pritzker_heights_of_polynomials_over_2021.pdf | |
dc.identifier.doi | 10.48550/arXiv.2101.06708 | |
dc.description.department | Mathematics | |
dc.type.genre | Preprint | |
dc.type.material | Text | |
dc.subject.keywords | algebraic integers | |
dc.subject.keywords | heights | |
dc.subject.keywords | integer polynomials | |
dc.subject.keywords | integer Chebyshev problem | |
dc.identifier.author | ORCID: 0000-0002-3102-5003 (Pritsker, Igor) | |
dc.identifier.author | ScopusID: 6602900239 (Pritsker, Igor) | |