Related papers: A lower bound on the canonical height for polynomi…

Let K be a function field in one variable over an arbitrary field F. Given a rational function f(z) in K(z) of degree at least two, the associated canonical height on the projective line was defined by Call and Silverman. The preperiodic…

Answering a question posed by Adam Epstein, we show that the collection of conjugacy classes of polynomials admitting a parabolic fixed point and at most one infinite critical orbit is a set of bounded height in the relevant moduli space.…

In this note, we provide a wide range of upper bounds for the moduli of the zeros of a complex polynomial. The obtained bounds complete a series of previous papers on the location of zeros of polynomials.

For a large prime $p$, and a polynomial $f$ over a finite field $F_p$ of $p$ elements, we obtain a lower bound on the size of the multiplicative subgroup of $F_p^*$ containing $H\ge 1$ consecutive values $f(x)$, $x = u+1, \ldots, u+H$,…

We prove an upper bound for the number of rational points of bounded height on irreducible affine hypersurfaces. More precisely, given an irreducible polynomial $f \in \mathbb{Z}[X_1, \dots, X_n]$, we prove an upper bound on the number of…

Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…

We construct an explicit lower bound for the volume of a complex hyperbolic orbifold that depends only on dimension.

We consider upper and lower bounds on the minimal height of an irrational number lying in a particular real quadratic field.

Explicit monoid structure is provided for the class of canonical subfield preserving polynomials over finite fields. Some classical results and asymptotic estimates will follow as corollaries.

Classes of polynomial differential equations of degree n are considered. An explicit upper bound on the size of the coefficients are given which implies that each equation in the class has exactly n complex periodic solutions. In most of…

We provide a lower bound on the probability that a binomial random variable is exceeding its mean. Our proof employs estimates on the mean absolute deviation and the tail conditional expectation of binomial random variables.

For any finite field $\mathbb{F}$ and any positive integer $n$ we count the number of monic polynomials of degree $n$ over $\mathbb{F}$ with nonzero constant coefficient and a self-reciprocal factor of any specified degree. An application…

We show the existence of canonical heights of subvarieties for bounded sequences of morphisms and give some applications.

We obtain explicit upper bounds for the number of irreducible factors for a class of compositions of polynomials in several variables over a given field. In particular, some irreducibility criteria are given for this class of compositions…

We prove, for the canonical height defined by Silverman [15] on monomial maps, the existence of effective lower bounds for heights of points with Zariski dense orbit, for cases with endomorphisms induced by matrices with real Jordan form.

We give lower bounds on the number of effective divisors of degree $\leq g-1$ with respect to the number of places of certain degrees of an algebraic function field of genus $g$ defined over a finite field. We deduce lower bounds and…

We establish a version of the Pommerenke-Levin-Yoccoz inequality for the modulus of a polynomial-like restriction of a global polynomial and give two applications. First it is shown that if the modulus of a polynomial-like restriction of an…

We study lower bounds for the self-intersection of the canonical divisor of "canonical varieties" (i.e. varieties whose canonical linear system gives a birational map). We give some improvements for the known results in the case of surfaces…

We explicitly find lower bounds on the volume of threefolds and fourfolds of general type in order to have nonvanishing of pluricanonical systems and birationality of pluricanonical maps. In the case of threefolds of large volume, we also…

Denis associated to each Drinfeld module M over a global function function field L a canonical height function, which plays a role analogous to that of the Neron-Tate height in the context of elliptic curves. We prove that there exist…