On the distribution of polynomials with bounded roots, Ⅰ. Polynomials with real coefficients

Shigeki Akiyama; Attila Pethoe

首页> 外文期刊>Journal of the Mathematical Society of Japan >On the distribution of polynomials with bounded roots, Ⅰ. Polynomials with real coefficients

【24h】

On the distribution of polynomials with bounded roots, Ⅰ. Polynomials with real coefficients

机译：关于有界根多项式的分布，Ⅰ。具有实系数的多项式

获取原文

获取原文并翻译 | 示例

掌桥外文数据库（机构版） >>

开具论文收录证明 >>

文献代查 >>

页面导航

摘要
著录项
相似文献
相关主题

摘要

Let v_d~((s)) denote the set of coefficient vectors of contractive polynomials of degree d with 2s non-real zeros. We prove that v_d~((s)) 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_d~((s)) 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.

机译：令v_d〜（（s））表示具有2s个非实数零的度为d的压缩多项式的系数向量的集合。我们证明v_d〜（（s））可以通过多重积分计算，这与Selberg积分及其推广有关。我们证明上述集合的边界是有限多个代数曲面的并集。我们研究v_d〜（（s））的算术性质，并证明它们是有理数。我们将证明，在压缩多项式中，选择完全实多项式的“概率”在其阶数变大时会迅速降低。

著录项

来源
《Journal of the Mathematical Society of Japan》 |2014年第3期|927-949|共23页
作者
Shigeki Akiyama; Attila Pethoe;
展开▼
作者单位

Institute of Mathematics University of Tsukuba 1-1-1 Tennodai, Tsukuba Ibaraki 350-0006, Japan;

Department of Computer Science University of Debrecen H-4010 Debrecen P.O. Box 12, Hungary;

展开▼
收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Selberg integral; polynomials with bounded roots;

机译：塞尔伯格积分;有限根的多项式;

相似文献

外文文献
中文文献
专利

1. Gale duality bounds for roots of polynomials with nonnegative coefficients [J] . Pfeifle J. Journal of Combinatorial Theory, Series A . 2010,第3期

机译：具有非负系数的多项式根的Gale对偶边界
2. ROOTS OF RANDOM POLYNOMIALS WITH COEFFICIENTS OF POLYNOMIAL GROWTH [J] . Do Yen, Oanh Nguyen, Vu Van The Annals of Probability: An Official Journal of the Institute of Mathematical Statistics . 2018,第5期

机译：随机多项式与多项式生长系数的根
3. Algorithm for Calculating the Roots of Polynomials with Coefficients in the Ring of Polynomials over an Arbitrary Integral Domain [J] . A. E. Maevskii Mathematical notes . 2009,第1a2期

机译：任意整数域上具有多项式环中多项式的根的计算算法
4. Bounds for Real Roots and Applications to Orthogonal Polynomials [C] . Doru Stefanescu International Workshop on Computer Algebra in Scientific Computing(CASC 2007); 20070916-20; Bonn(DE) . 2007

机译：实根的界线和正交多项式的应用
5. CLASSIFICATION OF ALL THE MINIMAL BILINEAR ALGORITHMS FOR COMPUTING THE COEFFICIENTS OF TWO POLYNOMIALS MODULO A POLYNOMIAL [D] . AVERBUCH, AMIR. 1984

机译：所有最小双线性算法的分类，用于计算两种多项式模数的系数多项式
6. On the Connection Coefficients of the Chebyshev-Boubaker Polynomials [O] . Paul Barry 2013

机译：Chebyshev-Boubaker多项式的连接系数
7. On the distribution of polynomials with bounded roots, I. Polynomials with real coefficients [O] . AKIYAMA Shigeki, PETHŐ Attila 2014

机译：关于有根的多项式的分布，I。实系数的多项式
8. ROUTINE FOR IMPROVING THE ACCURACY OF THE ROOTS OF POLYNOMIALS WITH REAL COEFFICIENTS [R] . Alene K. Depue 1965

机译：用真实系数提高多项式根的精度的常规

On the distribution of polynomials with bounded roots, Ⅰ. Polynomials with real coefficients

摘要

著录项

相似文献

相关主题

期刊订阅