Results 21 to 30 of about 520 (86)
Some inequalities and an application of exponential polynomials
, 2020 In the paper, with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem for the Stirling numbers of the first and second kinds, the author presents an explicit formula and an identity for ...
Feng Qi (祁锋)
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Some special finite sums related to the three-term polynomial relations and their applications
Advances in Differential Equations, 2014 We define some finite sums which are associated with the Dedekind type sums and Hardy-Berndt type sums. The aim of this paper is to prove a reciprocity law for one of these sums. Therefore, we define a new function which is related to partial derivatives
Elif Çeti̇n, Y. Simsek, I. N. Cangul
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A new bound on cofactors of sparse polynomials
Forum of Mathematics, SigmaWe prove that for polynomials $ f, g, h \in \mathbb {Z}[x] $ satisfying $ f = gh $ and $ f(0) \neq 0 $ , the $\ell _2$ -norm of the cofactor $ h $ is bounded by $$ \begin{align*} \left\Vert {h} \right\Vert{}_2\leq ...
Ido Nahshon, Amir Shpilka
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Squarefree values of polynomial discriminants II
Forum of Mathematics, PiWe determine the density of integral binary forms of given degree that have squarefree discriminant, proving for the first time that the lower density is positive. Furthermore, we determine the density of integral binary forms that cut out maximal orders
Manjul Bhargava +2 more
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Root multiplicities and number of nonzero coefficients of a polynomial
, 2005 It is known that the weight (that is, the number of nonzero coefficients) of a univariate polynomial over a field of characteristic zero is larger than the multiplicity of any of its nonzero roots.
Brindza B., Mattarei S., SANDRO MATTAREI
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Feasibility of primality in bounded arithmetic
Forum of Mathematics, SigmaWe prove the correctness of the AKS algorithm [1] within the bounded arithmetic theory $T^{\text {count}}_2$ or, equivalently, the first-order consequences of the theory $\text {VTC}^0$ expanded by the smash function, which we denote by
Raheleh Jalali, Ondřej Ježil
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Improvements on dimension growth results and effective Hilbert’s irreducibility theorem
Forum of Mathematics, SigmaWe sharpen and generalize the dimension growth bounds for the number of points of bounded height lying on an irreducible algebraic variety of degree d, over any global field.
Raf Cluckers +4 more
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Integral orthogonal bases of small height for real polynomial spaces [PDF]
, 2009 Let $P_N(R)$ be the space of all real polynomials in $N$ variables with the usual inner product $$ on it, given by integrating over the unit sphere. We start by deriving an explicit combinatorial formula for the bilinear form representing this inner ...
Fukshansky, Lenny
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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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