Results 11 to 20 of about 520 (86)
Sums of Powers and Special Polynomials
Discussiones Mathematicae - General Algebra and Applications, 2020 In this paper, we discuss sums of powers 1p + 2p + + np and compute both the exponential and ordinary generating functions for these sums. We express these generating functions in terms of exponential and geometric polynomials and also show their ...
Boyadzhiev Khristo N.
doaj +1 more source
Multivariable polynomial injections on rational numbers [PDF]
, 2010 For each number field k, the Bombieri-Lang conjecture for k-rational points on surfaces of general type implies the existence of a polynomial f(x,y) in k[x,y] inducing an injection k x k --> k.Comment: 4 ...
Poonen, Bjorn
core +3 more sources
A construction of integer-valued polynomials with prescribed sets of lengths of factorizations [PDF]
, 2013 For an arbitrary finite set S of natural numbers greater 1, we construct an integer-valued polynomial f, whose set of lengths in Int(Z) is S. The set of lengths of f is the set of all natural numbers n, such that f has a factorization as a product of n ...
Ch Frei +4 more
core +2 more sources
, 2010 The $q$-binomial coefficients $\qbinom{n}{m}=\prod_{i=1}^m(1-q^{n-m+i})/(1-q^i)$, for integers $0\le m\le n$, are known to be polynomials with non-negative integer coefficients.
Warnaar, S. Ole, Zudilin, Wadim
core +1 more source
A determinant formula for sums of powers of integers
, 2014 In this note, we first derive a recursive formula for the sum of powers Sk(n) = 1 k + 2k + · · · + nk, with k and n non-negative integers. We then apply it to establish, via Cramer’s rule, an explicit determinant formula for Sk(n) involving the Bernoulli
J. Cereceda
semanticscholar +1 more source
On some special Legendre sums of the form
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017 We prove that sums of the form with f(X), g(X) ∈ ℤ[X] can be explicitly computed whenever f and g are subject to some certain conditions which are defined in the paper.
Andrica Dorin, Crişan Vlad
doaj +1 more source
, 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
core +1 more source
Polynomials with a sharp Cauchy bound and their zeros of maximal modulus
, 2015 The moduli of zeros of a complex polynomial are bounded by the positive zero of an associated auxiliary polynomial. The bound is due to Cauchy. This note describes polynomials with a sharp Cauchy bound and the location of peripheral zeros.
H. K. Wimmer
semanticscholar +1 more source
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
core +2 more sources
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
core +1 more source