Add to ORKGWe study p-adic root separation for quadratic and cubic polynomials with integer coefficients. The quadratic and reducible cubic polynomials are completely understood, while in the irreducible cubic case and p ≠ 2, we give a family of polynomials with the bound which is the best currently known
The minimum root separation of an arbitrary polynomial P is defined as the minimum of the distances ...
AbstractWe present algorithms revealing new families of polynomials admitting sub-exponential detect...
We study bounds on the distances of roots of integer polynomials and applications of such results. T...
We study p-adic root separation for quadratic and cubic polynomials with integer coefficients. The q...
We study root separation of reducible monic integer polynomials of odd degree. Let H(P) be the naïve...
AbstractIn vol. 32 of this Journal, G.E. Collins reported on extensive calculations supporting his c...
AbstractA lower bound for the number of integer polynomials which simultaneously have “close” comple...
International audienceThe absolute separation of a polynomial is the minimum nonzero difference betw...
We present an implemented algorithmic method for counting and isolating all p-adic roots of univaria...
AbstractWe study a discrete optimization problem introduced by Babai, Frankl, Kutin, and Štefankovič...
A Diophantine problem means to find all solutions of an equation or system of equations in integers,...
Best paper awardInternational audienceIn this paper we derive aggregate separation bounds, named aft...
The improved bound bound that was claimed in an earlier version is removed, since there was an error...
Let n∈N be fixed, Q>1 be a real parameter and Pn(Q) denote the set of polynomials over Z of degree n...
An upper bound for the number of cubic polynomials which have small discriminant in terms of the Euc...
The minimum root separation of an arbitrary polynomial P is defined as the minimum of the distances ...
AbstractWe present algorithms revealing new families of polynomials admitting sub-exponential detect...
We study bounds on the distances of roots of integer polynomials and applications of such results. T...
We study p-adic root separation for quadratic and cubic polynomials with integer coefficients. The q...
We study root separation of reducible monic integer polynomials of odd degree. Let H(P) be the naïve...
AbstractIn vol. 32 of this Journal, G.E. Collins reported on extensive calculations supporting his c...
AbstractA lower bound for the number of integer polynomials which simultaneously have “close” comple...
International audienceThe absolute separation of a polynomial is the minimum nonzero difference betw...
We present an implemented algorithmic method for counting and isolating all p-adic roots of univaria...
AbstractWe study a discrete optimization problem introduced by Babai, Frankl, Kutin, and Štefankovič...
A Diophantine problem means to find all solutions of an equation or system of equations in integers,...
Best paper awardInternational audienceIn this paper we derive aggregate separation bounds, named aft...
The improved bound bound that was claimed in an earlier version is removed, since there was an error...
Let n∈N be fixed, Q>1 be a real parameter and Pn(Q) denote the set of polynomials over Z of degree n...
An upper bound for the number of cubic polynomials which have small discriminant in terms of the Euc...
The minimum root separation of an arbitrary polynomial P is defined as the minimum of the distances ...
AbstractWe present algorithms revealing new families of polynomials admitting sub-exponential detect...
We study bounds on the distances of roots of integer polynomials and applications of such results. T...