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On the distribution of polynomials with bounded roots, I. Polynomials with real coefficients
http://hdl.handle.net/2241/00125658
http://hdl.handle.net/2241/00125658e2d34063-f796-486c-bb05-521172ba0869
名前 / ファイル | ライセンス | アクション |
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JMSJ_66-3 (273.0 kB)
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Item type | Journal Article(1) | |||||
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公開日 | 2015-08-05 | |||||
タイトル | ||||||
タイトル | On the distribution of polynomials with bounded roots, I. Polynomials with real coefficients | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | journal article | |||||
著者 |
AKIYAMA, Shigeki
× AKIYAMA, Shigeki× PETHŐ, Attila |
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著者別名 |
秋山, 茂樹
× 秋山, 茂樹 |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | Let v(s)d denote the set of coefficient vectors of contractive polynomials of degree d with 2s non-real zeros.We prove that v(s)d can be computed by a multiple integral, which is related to the Selberg integral and its generalizations. We show that the boundary of the above set is the union of finitely many algebraic surfaces. We investigate arithmetical properties of v(s)d and prove among others that they are rational numbers. We will show that within contractive polynomials, the ‘probability’ of picking a totally real polynomial decreases rapidly when its degree becomes large. | |||||
書誌情報 |
Journal of the Mathematical Society of Japan 巻 66, 号 3, p. 927-949, 発行日 2014-07 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0025-5645 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA0070177X | |||||
DOI | ||||||
識別子タイプ | DOI | |||||
関連識別子 | 10.2969/jmsj/06630927 | |||||
権利 | ||||||
権利情報 | © 2014 The Mathematical Society of Japan | |||||
著者版フラグ | ||||||
値 | publisher | |||||
出版者 | ||||||
出版者 | The Mathematical Society of Japan |