On the periodicity of continued fractions in elliptic fields
Article [1] raised the question of the finiteness of the number of square-free polynomials f ∈ ℚ[ h ] of fixed degree for which f has periodic continued fraction expansion in the field ℚ(( h )) and the fields ℚ( h )( f ) are not isomorphic to one another and to fields of the form ℚ( h ) ( c h n + 1...
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| Veröffentlicht in: | Doklady. Mathematics 2017-07, Vol.96 (1), p.332-335 |
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| container_title | Doklady. Mathematics |
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| creator | Platonov, V. P. Fedorov, G. V. |
| description | Article [1] raised the question of the finiteness of the number of square-free polynomials
f
∈ ℚ[
h
] of fixed degree for which
f
has periodic continued fraction expansion in the field ℚ((
h
)) and the fields ℚ(
h
)(
f
) are not isomorphic to one another and to fields of the form ℚ(
h
)
(
c
h
n
+
1
)
, where
c
∈ ℚ* and
n
∈ ℕ. In this paper, we give a positive answer to this question for an elliptic field ℚ(
h
)(
f
) in the case deg
f
= 3. |
| doi_str_mv | 10.1134/S1064562417040068 |
| format | Article |
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f
∈ ℚ[
h
] of fixed degree for which
f
has periodic continued fraction expansion in the field ℚ((
h
)) and the fields ℚ(
h
)(
f
) are not isomorphic to one another and to fields of the form ℚ(
h
)
(
c
h
n
+
1
)
, where
c
∈ ℚ* and
n
∈ ℕ. In this paper, we give a positive answer to this question for an elliptic field ℚ(
h
)(
f
) in the case deg
f
= 3.</description><identifier>ISSN: 1064-5624</identifier><identifier>EISSN: 1531-8362</identifier><identifier>DOI: 10.1134/S1064562417040068</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Mathematics ; Mathematics and Statistics</subject><ispartof>Doklady. Mathematics, 2017-07, Vol.96 (1), p.332-335</ispartof><rights>Pleiades Publishing, Ltd. 2017</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-acbf552591930b85861718188663f136fc68a24bbcc0d5db35bab7f8adf5a8643</citedby><cites>FETCH-LOGICAL-c316t-acbf552591930b85861718188663f136fc68a24bbcc0d5db35bab7f8adf5a8643</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/S1064562417040068$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S1064562417040068$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Platonov, V. P.</creatorcontrib><creatorcontrib>Fedorov, G. V.</creatorcontrib><title>On the periodicity of continued fractions in elliptic fields</title><title>Doklady. Mathematics</title><addtitle>Dokl. Math</addtitle><description>Article [1] raised the question of the finiteness of the number of square-free polynomials
f
∈ ℚ[
h
] of fixed degree for which
f
has periodic continued fraction expansion in the field ℚ((
h
)) and the fields ℚ(
h
)(
f
) are not isomorphic to one another and to fields of the form ℚ(
h
)
(
c
h
n
+
1
)
, where
c
∈ ℚ* and
n
∈ ℕ. In this paper, we give a positive answer to this question for an elliptic field ℚ(
h
)(
f
) in the case deg
f
= 3.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>1064-5624</issn><issn>1531-8362</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kEtLAzEUhYMoWKs_wF3A9WhuXk3BjRRfUOhCXQ9JJtGUMTMmmUX_vSl1IYire-Cc8104CF0CuQZg_OYFiORCUg4LwgmR6gjNQDBoFJP0uOpqN3v_FJ3lvCWEC0rIDN1uIi4fDo8uhaELNpQdHjy2QywhTq7DPmlbwhAzDhG7vg9jCRb74Poun6MTr_vsLn7uHL093L-unpr15vF5dbduLANZGm2NF4KKJSwZMUooCQtQoJSUzAOT3kqlKTfGWtKJzjBhtFl4pTsvtJKczdHVgTum4WtyubTbYUqxvmwrUiwpqcSagkPKpiHn5Hw7pvCp064F0u5Hav-MVDv00Mk1G99d-kX-t_QNWvhnmw</recordid><startdate>20170701</startdate><enddate>20170701</enddate><creator>Platonov, V. P.</creator><creator>Fedorov, G. V.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170701</creationdate><title>On the periodicity of continued fractions in elliptic fields</title><author>Platonov, V. P. ; Fedorov, G. V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-acbf552591930b85861718188663f136fc68a24bbcc0d5db35bab7f8adf5a8643</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Platonov, V. P.</creatorcontrib><creatorcontrib>Fedorov, G. V.</creatorcontrib><collection>CrossRef</collection><jtitle>Doklady. Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Platonov, V. P.</au><au>Fedorov, G. V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the periodicity of continued fractions in elliptic fields</atitle><jtitle>Doklady. Mathematics</jtitle><stitle>Dokl. Math</stitle><date>2017-07-01</date><risdate>2017</risdate><volume>96</volume><issue>1</issue><spage>332</spage><epage>335</epage><pages>332-335</pages><issn>1064-5624</issn><eissn>1531-8362</eissn><abstract>Article [1] raised the question of the finiteness of the number of square-free polynomials
f
∈ ℚ[
h
] of fixed degree for which
f
has periodic continued fraction expansion in the field ℚ((
h
)) and the fields ℚ(
h
)(
f
) are not isomorphic to one another and to fields of the form ℚ(
h
)
(
c
h
n
+
1
)
, where
c
∈ ℚ* and
n
∈ ℕ. In this paper, we give a positive answer to this question for an elliptic field ℚ(
h
)(
f
) in the case deg
f
= 3.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S1064562417040068</doi><tpages>4</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1064-5624 |
| ispartof | Doklady. Mathematics, 2017-07, Vol.96 (1), p.332-335 |
| issn | 1064-5624 1531-8362 |
| language | eng |
| recordid | cdi_proquest_journals_1935920617 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Mathematics Mathematics and Statistics |
| title | On the periodicity of continued fractions in elliptic fields |
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