On Sendov's Conjecture

被引:1
|
作者
Sofi, G. M. [1 ]
Shah, W. M. [1 ]
机构
[1] Cent Univ Kashmir, Dept Math, Ganderbal 191201, India
关键词
Polynomials; Zeros; Critical points; POLYNOMIALS;
D O I
10.1007/s12215-021-00690-y
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Sendov's Conjecture asserts that if all the zeros of a polynomial p lie inside the closed unit disk then a closed unit disk centered at each of its zeros contains a critical point of p . In this paper, we show that the Sendov's Conjecture holds for a polynomial if all its zeros lie on a line or a circle inside the unit disk.
引用
收藏
页码:493 / 497
页数:5
相关论文
共 50 条
  • [21] Chui's conjecture in Bergman spaces
    Abakumov, Evgeny
    Borichev, Alexander
    Fedorovskiy, Konstantin
    MATHEMATISCHE ANNALEN, 2021, 379 (3-4) : 1507 - 1532
  • [22] Sidorenko's conjecture, colorings and independent sets
    Csikvari, Peter
    Lin, Zhicong
    ELECTRONIC JOURNAL OF COMBINATORICS, 2017, 24 (01)
  • [23] TOWARDS VAN DER WAERDEN?S CONJECTURE
    Chow, Sam
    Dietmann, Rainer
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2023, 376 (04) : 2739 - 2785
  • [24] A Short Proof of Moll's Minimal Conjecture
    Lv, Lun
    ELECTRONIC JOURNAL OF COMBINATORICS, 2017, 24 (04)
  • [25] Lusztig's conjecture as a moment graph problem
    Fiebig, Peter
    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2010, 42 : 957 - 972
  • [26] The negative answer to Kameko's conjecture on the hit problem
    Nguyen Sum
    ADVANCES IN MATHEMATICS, 2010, 225 (05) : 2365 - 2390
  • [27] Any counterexample to Makienko's conjecture is an indecomposable continuum
    Curry, Clinton P.
    Mayer, John C.
    Meddaugh, Jonathan
    Rogers, James T., Jr.
    ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2009, 29 : 875 - 883
  • [28] On generalisation of Brown's conjecture
    Nazir, Ishfaq
    Mir, Mohammad Ibrahim
    Wani, Irfan Ahmad
    INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2021, 12 (02): : 1151 - 1155
  • [29] On a Conjecture of S. Stahl
    Chen, Yichao
    Liu, Yanpei
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2010, 62 (05): : 1058 - 1059
  • [30] Disproving Hooley's conjecture
    Fiorilli, Daniel
    Martin, Greg
    JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2023, 25 (12) : 4791 - 4812