Related papers: The resultant divisor is negative

We investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation (PLDE). Two kinds of polynomials are to be distinguished, we call them /periodic/ and…

We show that the implicit equation of a surface in 3-dimensional projective space parametrized by bi-homogeneous polynomials of bi-degree (d,d), for a given positive integer d, can be represented and computed from the linear syzygies of its…

The space of polynomials in two real variables with values in a 2-dimensional irreducible module of a dihedral group is studied as a standard module for Dunkl operators. The one-parameter case is considered (omitting the two-parameter case…

We observe that the E-resultant of a very ample rank 2 vector bundle E on a real projective curve (with no real points) is nonnegative when restricted to the space of real sections. Moreover, we show that if E has a section vanishing at…

The decomposition of polynomials of one vector variable into irreducible modules for the orthogonal group is a crucial result in harmonic analysis which makes use of the Howe duality theorem and leads to the study of spherical harmonics.…

The classical modular polynomial for $j$-invariants describes the relation between two elliptic curves connected by isogenies. This polynomial has been applied to various algorithms in computational number theory, such as point counting on…

The multivariate resultant is a fundamental tool of computational algebraic geometry. It can in particular be used to decide whether a system of n homogeneous equations in n variables is satisfiable (the resultant is a polynomial in the…

The resultant of two univariate polynomials is an invariant of great importance in commutative algebra and vastly used in computer algebra systems. Here we present an algorithm to compute it over Artinian principal rings with a modified…

We study M(n), the number of distinct values taken by multinomial coefficients with upper entry n, and some closely related sequences. We show that both pP(n)/M(n) and M(n)/p(n) tend to zero as n goes to infinity, where pP(n) is the number…

Let $\chi$ be an order $c$ multiplicative character of a finite field and $f(x)=x^d+\lambda x^e$ a binomial with $(d,e)=1$. We study the twisted classical and $T$-adic Newton polygons of $f$. When $p>(d-e)(2d-1)$, we give a lower bound of…

We consider polynomial equations, or systems of polynomial equations, with integer coefficients, modulo prime numbers $p$. We offer an elementary approach based on a counting method. The outcome is a weak form of the Lang-Weil lower bound…

In this paper, we consider modular local polynomials. These functions satisfy modularity while they are locally defined as polynomials outside of an exceptional set. We prove an inequality for the dimension of the space of such forms when…

In this paper, we study the derivatives of an integer-valued polynomial of a given degree. Denoting by $E_n$ the set of the integer-valued polynomials with degree $\leq n$, we show that the smallest positive integer $c_n$ satisfying the…

In this paper we study the question of whether on smooth projective surfaces the denominators in the volumes of big line bundles are bounded. In particular we investigate how this condition is related to bounded negativity (i.e., the…

We improve Mahler's lower bound for the Mahler measure in terms of the discriminant and degree for a specific class of polynomials: complex monic polynomials of degree $d\geq 2$ such that all roots with modulus greater than some fixed value…

We address a long-standing and long-investigated problem in combinatorial topology, and break the exponential barrier for triangulations of real projective space, constructing a trianglation of $\mathbb{RP}^n$ of size…

We define a combinatorial object that can be associated with any conic-line arrangement with ordinary singularities, which we call the combinatorial Poincar\'e polynomial. We prove a Terao-type factorization statement on the splitting of…

For $\epsilon$-lc Fano type varieties $X$ of dimension $d$ and a given finite set $\Gamma$, we show that there exists a positive integer $m_0$ which only depends on $\epsilon,d$ and $\Gamma$, such that both $|-mK_X-\sum_i\lceil mb_i\rceil…

We study a family of polynomials which are orthogonal with respect to the varying, highly oscillatory complex weight function $e^{ni\lambda z}$ on $[-1,1]$, where $\lambda$ is a positive parameter. This family of polynomials has appeared in…

A polynomial of degree $n$ in two variables is shown to be uniquely determined by its Radon projections taken over $[n/2]+1$ parallel lines in each of the $(2[(n+1)/2]+1)$ equidistant directions along the unit circle.