On Wirsing's problem in small exact degree
Mosc. Math. J. 24 (2024), no. 3, 461-489 We investigate a variant of Wirsing's problem on approximation to a real number by real algebraic numbers of degree exactly $n$. This has been studied by Bugeaud and Teulie. We improve their bounds for degrees up to $n=7$. Moreover, we obtain results reg...
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| creator | Schleischitz, Johannes |
| description | Mosc. Math. J. 24 (2024), no. 3, 461-489 We investigate a variant of Wirsing's problem on approximation to a real
number by real algebraic numbers of degree exactly $n$. This has been studied
by Bugeaud and Teulie. We improve their bounds for degrees up to $n=7$.
Moreover, we obtain results regarding small values of polynomials and
approximation to a real number by algebraic integers in small prescribed
degree. The main ingredient are irreducibility criteria for integral linear
combinations of coprime integer polynomials. Moreover, for cubic polynomials
these criteria improve results of Gy\H{o}ry on a problem of Szegedy. |
| doi_str_mv | 10.48550/arxiv.2108.01484 |
| format | Article |
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number by real algebraic numbers of degree exactly $n$. This has been studied
by Bugeaud and Teulie. We improve their bounds for degrees up to $n=7$.
Moreover, we obtain results regarding small values of polynomials and
approximation to a real number by algebraic integers in small prescribed
degree. The main ingredient are irreducibility criteria for integral linear
combinations of coprime integer polynomials. Moreover, for cubic polynomials
these criteria improve results of Gy\H{o}ry on a problem of Szegedy.</description><identifier>DOI: 10.48550/arxiv.2108.01484</identifier><language>eng</language><subject>Mathematics - Number Theory</subject><creationdate>2021-08</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2108.01484$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2108.01484$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Schleischitz, Johannes</creatorcontrib><title>On Wirsing's problem in small exact degree</title><description>Mosc. Math. J. 24 (2024), no. 3, 461-489 We investigate a variant of Wirsing's problem on approximation to a real
number by real algebraic numbers of degree exactly $n$. This has been studied
by Bugeaud and Teulie. We improve their bounds for degrees up to $n=7$.
Moreover, we obtain results regarding small values of polynomials and
approximation to a real number by algebraic integers in small prescribed
degree. The main ingredient are irreducibility criteria for integral linear
combinations of coprime integer polynomials. Moreover, for cubic polynomials
these criteria improve results of Gy\H{o}ry on a problem of Szegedy.</description><subject>Mathematics - Number Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzrsKwjAUgOEsDqI-gJPZBKE1l5OYjiLeQHARHMtpLhJoq6Qi-vbiZfq3n4-QMWc5GKXYHNMzPnLBmckZBwN9Mju29BxTF9vLtKO3dK1q39DY0q7Buqb-ifZOnb8k74ekF7Du_OjfATlt1qfVLjsct_vV8pChXkDmgleglUUoKgZgi8JKI4JlTnMtlAoWhZYiSAfOFxyldLxyoeICuTMM5YBMftsvtryl2GB6lR90-UXLNzGBO4M</recordid><startdate>20210803</startdate><enddate>20210803</enddate><creator>Schleischitz, Johannes</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20210803</creationdate><title>On Wirsing's problem in small exact degree</title><author>Schleischitz, Johannes</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a674-dfe5465ca49b044c99c382fc0d616255fca2632f3d4de91a33d1bdfb12a1d80a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Mathematics - Number Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Schleischitz, Johannes</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Schleischitz, Johannes</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Wirsing's problem in small exact degree</atitle><date>2021-08-03</date><risdate>2021</risdate><abstract>Mosc. Math. J. 24 (2024), no. 3, 461-489 We investigate a variant of Wirsing's problem on approximation to a real
number by real algebraic numbers of degree exactly $n$. This has been studied
by Bugeaud and Teulie. We improve their bounds for degrees up to $n=7$.
Moreover, we obtain results regarding small values of polynomials and
approximation to a real number by algebraic integers in small prescribed
degree. The main ingredient are irreducibility criteria for integral linear
combinations of coprime integer polynomials. Moreover, for cubic polynomials
these criteria improve results of Gy\H{o}ry on a problem of Szegedy.</abstract><doi>10.48550/arxiv.2108.01484</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Number Theory |
| title | On Wirsing's problem in small exact degree |
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