scholarly journals On the connectivity of the hyperbolicity region of irreducible polynomials

2019 ◽  
Vol 19 (2) ◽  
pp. 231-233
Author(s):  
Mario Denis Kummer
Keyword(s):  
Hyperbolic Polynomial ◽  
Irreducible Polynomials ◽  
Hyperbolicity Region ◽  
Hyperbolicity Cones

Abstract We give a proof for the fact that an irreducible hyperbolic polynomial has only one pair of hyperbolicity cones. Apart from the use of Bertini’s Theorem the proof is elementary.

scholarly journals A new class of irreducible polynomials

2021 ◽  
pp. 1-6
Author(s):  
Jitender Singh ◽  
Sanjeev Kumar
Keyword(s):  
Irreducible Polynomials ◽  
New Class

Composite values of irreducible polynomials

2019 ◽  
Vol 74 (1) ◽  
pp. 36-37
Author(s):  
Franz Lemmermeyer
Keyword(s):  
Irreducible Polynomials

scholarly journals Multiplicative groups of fields and hereditarily irreducible polynomials

2016 ◽  
Vol 168 ◽  
pp. 452-471
Author(s):  
Alice Medvedev ◽  
Ramin Takloo-Bighash
Keyword(s):  
Irreducible Polynomials ◽  
Multiplicative Groups

The Number of Irreducible Polynomials and Lyndon Words with Given Trace

2001 ◽  
Vol 14 (2) ◽  
pp. 240-245 ◽  
Author(s):  
F. Ruskey ◽  
C. R. Miers ◽  
J. Sawada
Keyword(s):  
Irreducible Polynomials ◽  
Lyndon Words

Construction of hash functions based on theory of finite fields with the use of irreducible polynomials

2021 ◽  
Vol 143 (2) ◽  
pp. 66-76
Author(s):  
U.K. Turusbekova ◽  
◽  
S.A. Altynbek ◽  
A.S. Turginbayeva ◽  
L. Mereikhan ◽  
...  
Keyword(s):  
Finite Fields ◽  
Hash Functions ◽  
Irreducible Polynomials

Construction of Irreducible Polynomials

1993 ◽  
pp. 39-68
Author(s):  
Ian F. Blake ◽  
XuHong Gao ◽  
Ronald C. Mullin ◽  
Scott A. Vanstone ◽  
Tomik Yaghoobian
Keyword(s):  
Irreducible Polynomials

scholarly journals Real Zeros of a Class of Hyperbolic Polynomials with Random Coefficients

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Mina Ketan Mahanti ◽  
Amandeep Singh ◽  
Lokanath Sahoo
Keyword(s):  
Random Variables ◽  
Random Coefficients ◽  
Expected Number ◽  
Hyperbolic Polynomial ◽  
Gaussian Random Variables ◽  
Hyperbolic Polynomials ◽  
Asymptotic Value ◽  
Real Zeros ◽  
Number Of Real Zeros

We have proved here that the expected number of real zeros of a random hyperbolic polynomial of the formy=Pnt=n1a1cosh⁡t+n2a2cosh⁡2t+⋯+nnancosh⁡nt, wherea1,…,anis a sequence of standard Gaussian random variables, isn/2+op(1). It is shown that the asymptotic value of expected number of times the polynomial crosses the levely=Kis alson/2as long asKdoes not exceed2neμ(n), whereμ(n)=o(n). The number of oscillations ofPn(t)abouty=Kwill be less thann/2asymptotically only ifK=2neμ(n), whereμ(n)=O(n)orn-1μ(n)→∞. In the former case the number of oscillations continues to be a fraction ofnand decreases with the increase in value ofμ(n). In the latter case, the number of oscillations reduces toop(n)and almost no trace of the curve is expected to be present above the levely=Kifμ(n)/(nlogn)→∞.

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