Zobrazeno 1 - 10
of 366
pro vyhledávání: '"12e05"'
Autor:
Singh, Jitender
In this article, we obtain upper bounds on the number of irreducible factors of some classes of polynomials having integer coefficients, which in particular yield some of the well known irreducibility criteria. For devising our results, we use the in
Externí odkaz:
http://arxiv.org/abs/2411.18366
Autor:
Bary-Soroker, Lior, Shmueli, Roy
We study a random polynomial of degree $n$ over the finite field $\mathbb{F}_q$, where the coefficients are independent and identically distributed and uniformly chosen from the squares in $\mathbb{F}_q$. Our main result demonstrates that the likelih
Externí odkaz:
http://arxiv.org/abs/2410.16814
Autor:
Berceanu, Barbu Rudolf
We recall the fundamental theorem of J.F. Ritt, with a stress on the action of the affine group and canonical forms of complex polynomials. Then we give a complete presentation of the monoid $(\mathbb{C}\mbox{[X]},\circ)$. A list of decomposable poly
Externí odkaz:
http://arxiv.org/abs/2410.12447
Autor:
von Bothmer, Hans-Christian
Let $\omega$ be a plane autonomous system and C its configuration of algebraic integral curves. If the singularities of C are quasi homogeneous we give new conditions for existence of a Darboux integrating factor or a Darboux first integral. This is
Externí odkaz:
http://arxiv.org/abs/2409.01751
Autor:
Seguin, Béranger
Let $K$ be a field of characteristic $0$ and $k \geq 2$ be an integer. We prove that every $K$-linear bijection $f : K[X] \to K[X]$ strongly preserving the set of $k$-free polynomials (or the set of polynomials with a $k$-fold root in $K$) is a const
Externí odkaz:
http://arxiv.org/abs/2407.09118
Autor:
Edens, Oakley, Reichstein, Zinovy
The resolvent degree $\textrm{rd}_{\mathbb{C}}(n)$ is the smallest integer $d$ such that a root of the general polynomial $$f(x) = x^n + a_1 x^{n-1} + \ldots + a_n$$ can be expressed as a composition of algebraic functions in at most $d$ variables wi
Externí odkaz:
http://arxiv.org/abs/2406.15954
Autor:
Goksel, Vefa, Micheli, Giacomo
Let $q$ be an odd prime power. Let $f\in \mathbb{F}_q[x]$ be a polynomial having degree at least $2$, $a\in \mathbb{F}_q$, and denote by $f^n$ the $n$-th iteration of $f$. Let $\chi$ be the quadratic character of $\mathbb{F}_q$, and $\mathcal{O}_f(a)
Externí odkaz:
http://arxiv.org/abs/2403.19642
If a reduced bivariate polynomial is quasi-homogeneous, then its discriminant is a monomial. Over fields of characteristic $0$, we show that if one adds another simple condition, this becomes an equivalence. We also give a third equivalent condition
Externí odkaz:
http://arxiv.org/abs/2403.05324
Autor:
Ghosh, Soham
The Casas-Alvero conjecture predicts that every univariate polynomial over an algebraically closed field of characteristic zero sharing a common factor with each of its Hasse-Schmidt derivatives is a power of a linear polynomial. The conjecture for p
Externí odkaz:
http://arxiv.org/abs/2402.18717
Autor:
Yamada, Tomohiro
We give explicit upper bounds for coefficients of polynomials appearing in Gauss-Kra\"{i}tchik formula for cyclotomic polynomials. We use a certain relation between elementary symmetric polynomials and power sums polynomials.
Comment: 10 pages,
Comment: 10 pages,
Externí odkaz:
http://arxiv.org/abs/2402.15747