Results 11 to 20 of about 439 (37)
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
Root separation for reducible monic polynomials of odd degree [PDF]
, 2017 We study root separation of reducible monic integer polynomials of odd degree. Let h(P) be the naive height, sep(P) the minimal distance between two distinct roots of an integer polynomial P(x) and sep(P)=h(P)^{-e(P)}. Let e_r*(d)=limsup_{deg(P)=d, h(P)->
Dujella, Andrej, Pejkovic, Tomislav
core +3 more sources
A coprimality condition on consecutive values of polynomials [PDF]
, 2017 Let $f\in\mathbb{Z}[X]$ be quadratic or cubic polynomial. We prove that there exists an integer $G_f\geq 2$ such that for every integer $k\geq G_f$ one can find infinitely many integers $n\geq 0$ with the property that none of $f(n+1),f(n+2),\dots,f(n+k)$
Sanna, Carlo, Szikszai, Márton
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
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
core +3 more sources
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
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
core +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