Results 21 to 30 of about 485 (68)
Note on the number of divisors of reducible quadratic polynomials
, 2018 In a recent paper, Lapkova uses a Tauberian theorem to derive the asymptotic formula for the divisor sum $\sum_{n \leq x} d( n (n+v))$ where $v$ is a fixed integer and $d(n)$ denotes the number of divisors of $n$.
Dudek, Adrian W. +2 more
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, 2011 We show that there are at most $O_{n,\epsilon}(H^{n-2+\sqrt{2}+\epsilon})$ monic integer polynomials of degree $n$ having height at most $H$ and Galois group different from the full symmetric group $S_n$, improving on the previous 1973 world record $O_{n}
Dietmann, Rainer
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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)
semanticscholar +1 more source
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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Inequalities for Lorentz polynomials [PDF]
, 2014 We prove a few interesting inequalities for Lorentz polynomials including Nikolskii-type inequalities. A highlight of the paper is a sharp Markov-type inequality for polynomials of degree at most n with real coefficients and with derivative not vanishing
Erdelyi, Tamas
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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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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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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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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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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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