A remark on Zagier's observation of the Mandelbrot set
We investigate the arithmetic properties of the coefficients for the normalized conformal mapping of the exterior of the Multibrot set. In this paper, an estimate of the prime factor of the denominator of these coefficients is given. Bielefeld, Fisher and Haeseler presented Zagier's observation...
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| creator | Shimauchi, Hirokazu |
| description | We investigate the arithmetic properties of the coefficients for the
normalized conformal mapping of the exterior of the Multibrot set. In this
paper, an estimate of the prime factor of the denominator of these coefficients
is given. Bielefeld, Fisher and Haeseler presented Zagier's observation for the
growth of denominator of the coefficients for the Mandelbrot set and Yamashita
verified it in his master thesis. Our study takes into consideration both
Zagier's observation and Yamashita's estimate. |
| doi_str_mv | 10.48550/arxiv.1306.6140 |
| format | Article |
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normalized conformal mapping of the exterior of the Multibrot set. In this
paper, an estimate of the prime factor of the denominator of these coefficients
is given. Bielefeld, Fisher and Haeseler presented Zagier's observation for the
growth of denominator of the coefficients for the Mandelbrot set and Yamashita
verified it in his master thesis. Our study takes into consideration both
Zagier's observation and Yamashita's estimate.</description><identifier>DOI: 10.48550/arxiv.1306.6140</identifier><language>eng</language><subject>Mathematics - Complex Variables ; Mathematics - Dynamical Systems</subject><creationdate>2013-06</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>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1306.6140$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1306.6140$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Shimauchi, Hirokazu</creatorcontrib><title>A remark on Zagier's observation of the Mandelbrot set</title><description>We investigate the arithmetic properties of the coefficients for the
normalized conformal mapping of the exterior of the Multibrot set. In this
paper, an estimate of the prime factor of the denominator of these coefficients
is given. Bielefeld, Fisher and Haeseler presented Zagier's observation for the
growth of denominator of the coefficients for the Mandelbrot set and Yamashita
verified it in his master thesis. Our study takes into consideration both
Zagier's observation and Yamashita's estimate.</description><subject>Mathematics - Complex Variables</subject><subject>Mathematics - Dynamical Systems</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzj9vwjAQhnEvHRB0Z0LeOiW9s-MjGRFqAQnEwsQSnZMzjaCkciJUvj1_2umVnuHVT6kxQprlzsE7x9_mkqIFSgkzGCia6SjfHI-6Pes9HxqJb51ufSfxwn1zj23Q_ZfoDZ9rOfnY9rqTfqReAp86ef3fodp9fuzmy2S9Xazms3XC5CBBQ6aqjRHEKVDB6Auk2laUF95UjGQDgM_YW-fy2lMIxkDFQAYo80HsUE3-bp_u8ic2d-q1fPjLh9_eAO_QPpw</recordid><startdate>20130626</startdate><enddate>20130626</enddate><creator>Shimauchi, Hirokazu</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20130626</creationdate><title>A remark on Zagier's observation of the Mandelbrot set</title><author>Shimauchi, Hirokazu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a650-1262cd22e117069a1b916d3c689b2ca163f00b4ab3558db6ff220ca062064bfe3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Mathematics - Complex Variables</topic><topic>Mathematics - Dynamical Systems</topic><toplevel>online_resources</toplevel><creatorcontrib>Shimauchi, Hirokazu</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Shimauchi, Hirokazu</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A remark on Zagier's observation of the Mandelbrot set</atitle><date>2013-06-26</date><risdate>2013</risdate><abstract>We investigate the arithmetic properties of the coefficients for the
normalized conformal mapping of the exterior of the Multibrot set. In this
paper, an estimate of the prime factor of the denominator of these coefficients
is given. Bielefeld, Fisher and Haeseler presented Zagier's observation for the
growth of denominator of the coefficients for the Mandelbrot set and Yamashita
verified it in his master thesis. Our study takes into consideration both
Zagier's observation and Yamashita's estimate.</abstract><doi>10.48550/arxiv.1306.6140</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Complex Variables Mathematics - Dynamical Systems |
| title | A remark on Zagier's observation of the Mandelbrot set |
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