New Results on the Periodicity Problem for Continued Fractions of Elements of Hyperelliptic Fields
We study the problem of describing square-free polynomials of odd degree with periodic expansion of into a functional continued fraction in , where . We obtain a complete description of such polynomials that does not depend on the field and the degree of a polynomial, provided that the degree of the...
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| Veröffentlicht in: | Proceedings of the Steklov Institute of Mathematics 2023-03, Vol.320 (1), p.258-266 |
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| container_title | Proceedings of the Steklov Institute of Mathematics |
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| creator | Platonov, V. P. Petrunin, M. M. |
| description | We study the problem of describing square-free polynomials
of odd degree with periodic expansion of
into a functional continued fraction in
, where
. We obtain a complete description of such polynomials
that does not depend on the field
and the degree of a polynomial, provided that the degree
of the fundamental
-unit of the corresponding hyperelliptic field
either does not exceed
or is even and does not exceed
. |
| doi_str_mv | 10.1134/S008154382301011X |
| format | Article |
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of odd degree with periodic expansion of
into a functional continued fraction in
, where
. We obtain a complete description of such polynomials
that does not depend on the field
and the degree of a polynomial, provided that the degree
of the fundamental
-unit of the corresponding hyperelliptic field
either does not exceed
or is even and does not exceed
.</description><identifier>ISSN: 0081-5438</identifier><identifier>EISSN: 1531-8605</identifier><identifier>DOI: 10.1134/S008154382301011X</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>14/34 ; 639/766/189 ; 639/766/530 ; 639/766/747 ; Mathematics ; Mathematics and Statistics ; Polynomials</subject><ispartof>Proceedings of the Steklov Institute of Mathematics, 2023-03, Vol.320 (1), p.258-266</ispartof><rights>Pleiades Publishing, Ltd. 2023</rights><rights>Pleiades Publishing, Ltd. 2023.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-61836e6eec116248aaaa52d009391a25e644268e8cda4cf25ab64c83e675c6013</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S008154382301011X$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S008154382301011X$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>309,310,314,780,784,789,790,23930,23931,25140,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Platonov, V. P.</creatorcontrib><creatorcontrib>Petrunin, M. M.</creatorcontrib><title>New Results on the Periodicity Problem for Continued Fractions of Elements of Hyperelliptic Fields</title><title>Proceedings of the Steklov Institute of Mathematics</title><addtitle>Proc. Steklov Inst. Math</addtitle><description>We study the problem of describing square-free polynomials
of odd degree with periodic expansion of
into a functional continued fraction in
, where
. We obtain a complete description of such polynomials
that does not depend on the field
and the degree of a polynomial, provided that the degree
of the fundamental
-unit of the corresponding hyperelliptic field
either does not exceed
or is even and does not exceed
.</description><subject>14/34</subject><subject>639/766/189</subject><subject>639/766/530</subject><subject>639/766/747</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Polynomials</subject><issn>0081-5438</issn><issn>1531-8605</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1kM1Lw0AQxRdRsFb_AG8LnqM7-9XNUYq1QtHiB3gL6WaiW9Js3N0i_e9NrOBBnMsMvN97A4-Qc2CXAEJePTFmQElhuGDAAF4PyAiUgMxopg7JaJCzQT8mJzGuGZNqIvMRWd3jJ33EuG1SpL6l6R3pEoPzlbMu7egy-FWDG1r7QKe-Ta7dYkVnobTJ-ba31PSm17FN3_d812HApnFdcpbOHDZVPCVHddlEPPvZY_Iyu3mezrPFw-3d9HqRWa5NyjQYoVEjWgDNpSn7UbxiLBc5lFyhlrIH0diqlLbmqlxpaY1APVFWMxBjcrHP7YL_2GJMxdpvQ9u_LPhQi-G5HCjYUzb4GAPWRRfcpgy7AlgxVFn8qbL38L0n9mz7huE3-X_TF-gpdWA</recordid><startdate>20230301</startdate><enddate>20230301</enddate><creator>Platonov, V. P.</creator><creator>Petrunin, M. M.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20230301</creationdate><title>New Results on the Periodicity Problem for Continued Fractions of Elements of Hyperelliptic Fields</title><author>Platonov, V. P. ; Petrunin, M. M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-61836e6eec116248aaaa52d009391a25e644268e8cda4cf25ab64c83e675c6013</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>14/34</topic><topic>639/766/189</topic><topic>639/766/530</topic><topic>639/766/747</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Polynomials</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Platonov, V. P.</creatorcontrib><creatorcontrib>Petrunin, M. M.</creatorcontrib><collection>CrossRef</collection><jtitle>Proceedings of the Steklov Institute of Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Platonov, V. P.</au><au>Petrunin, M. M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>New Results on the Periodicity Problem for Continued Fractions of Elements of Hyperelliptic Fields</atitle><jtitle>Proceedings of the Steklov Institute of Mathematics</jtitle><stitle>Proc. Steklov Inst. Math</stitle><date>2023-03-01</date><risdate>2023</risdate><volume>320</volume><issue>1</issue><spage>258</spage><epage>266</epage><pages>258-266</pages><issn>0081-5438</issn><eissn>1531-8605</eissn><abstract>We study the problem of describing square-free polynomials
of odd degree with periodic expansion of
into a functional continued fraction in
, where
. We obtain a complete description of such polynomials
that does not depend on the field
and the degree of a polynomial, provided that the degree
of the fundamental
-unit of the corresponding hyperelliptic field
either does not exceed
or is even and does not exceed
.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S008154382301011X</doi><tpages>9</tpages></addata></record> |
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| subjects | 14/34 639/766/189 639/766/530 639/766/747 Mathematics Mathematics and Statistics Polynomials |
| title | New Results on the Periodicity Problem for Continued Fractions of Elements of Hyperelliptic Fields |
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