Results 21 to 30 of about 439 (37)
Squarefree values of polynomial discriminants II
Forum of Mathematics, PiWe determine the density of integral binary forms of given degree that have squarefree discriminant, proving for the first time that the lower density is positive. Furthermore, we determine the density of integral binary forms that cut out maximal orders
Manjul Bhargava +2 more
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Improvements on dimension growth results and effective Hilbert’s irreducibility theorem
Forum of Mathematics, SigmaWe sharpen and generalize the dimension growth bounds for the number of points of bounded height lying on an irreducible algebraic variety of degree d, over any global field.
Raf Cluckers +4 more
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Root separation for irreducible integer polynomials
, 2011 We establish new results on root separation of integer, irreducible polynomials of degree at least four. These improve earlier bounds of Bugeaud and Mignotte (for even degree) and of Beresnevich, Bernik, and Goetze (for odd degree).Comment: 8 pages ...
Bugeaud, Yann, Dujella, Andrej
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On the link between Binomial Theorem and Discrete Convolution of Polynomials
, 2020 Let $\mathbf{P}^{m}_{b}(x), \; m\in\mathbb{N}$ be a $2m+1$-degree integer-valued polynomial in $b,x\in\mathbb{R}$. In this manuscript we show that Binomial theorem is partial case of polynomial $\mathbf{P}^{m}_{b}(x)$. Furthermore, by means of $\mathbf{P}
Kolosov, Petro
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A Swan-like note for a family of binary pentanomials
, 2018 In this note, we employ the techniques of Swan (Pacific J. Math. 12(3): 1099-1106, 1962) with the purpose of studying the parity of the number of the irreducible factors of the penatomial $X^n+X^{3s}+X^{2s}+X^{s}+1\in\mathbb{F}_2[X]$, where $s$ is even ...
Kapetanakis, Giorgos
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Classification and irreducibility of a class of integer polynomials
Open MathematicsWe find all integer polynomials of degree dd that take the values ±1\pm 1 at exactly dd integer arguments, and determine the irreducibility of these polynomials by means of an elementary approach.
Chen Yizhi, Zhao Xiangui, Zhou Xuan
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Identities Involving Zeros of Ramanujan and Shanks Cubic Polynomials [PDF]
, 2014 In this paper we highlight the connection between Ramanujan cubic polynomials (RCPs) and a class of polynomials, the Shanks cubic polynomials (SCPs), which generate cyclic cubic fields.
Abrate, Marco +3 more
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Is there a polynomial D(2X + 1)-quadruple?
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria MatematicaIn this paper, we show that there does not exist a polynomial D(2X+ 1)-quadruple {a, b, c, d}, such that 0 < a < b < c < d and deg d = deg b.
Franušić Zrinka, Jurasić Ana
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Diophantine equations in separated variables and polynomial power sums. [PDF]
Mon Hefte Math, 2021 Fuchs C, Heintze S.
europepmc +1 more source