Related papers: 2-extensions with many points

We establish some upper and lower bounds for the number of rational points of Prym varieties over finite fields.

We establish coupled fixed point theorems for contraction involving rational expressions in partially ordered metric spaces.

We develop a theory of extensions of hyperfields that generalizes the notion of field extensions. Since hyperfields have a multivalued addition, we must consider two kinds of extensions that we call weak hyperfield extensions and strong…

We consider the expansion of the real field by the group of rational points of an elliptic curve over the rational numbers. We prove a completeness result, followed by a quantifier elimination result. Moreover we show that open sets…

A general type of ray class fields of global function fields is investigated. The systematic computation of their genera leads to new examples of curves over finite fields with comparatively many rational points.

A triangular field of rational numbers is characterized, with relations to Stirling numbers 2nd, Hyperbolic functions, and centered Binomial distribution. A Generating function is given.

We prove a few uniform versions of the Mordell-Lang Conjecture and of the Shafarevich Conjecture for curves over function fields and their rational points. The main focus is on function fields having high transcendence degree over the…

We give formulas for the number of polynomials over a finite field with given root multiplicities, in particular in cases when the formula is surprisingly simple (a power of q). Besides this concrete interpretation, we also prove an…

We prove finite field analogues of integral representations of Appell- Lauricella hypergeometric functions in many variables. We consider certain hypersurfaces having a group action and compute the numbers of rational points associated with…

Let $K$ be a field, $a, b\in K$ and $ab\neq 0$. Let us consider the polynomials $g_{1}(x)=x^n+ax+b, g_{2}(x)=x^n+ax^2+bx$, where $n$ is a fixed positive integer. In this paper we show that for each $k\geq 2$ the hypersurface given by the…

Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are…

The aim of this paper is to show that there exists a deterministic algorithm that can be applied to compute the factors of a polynomial of degree 2, defined over a finite field, given certain conditions.

We provide in this paper an upper bound for the number of rational points on a curve defined over a one variable function field over a finite field. The bound only depends on the curve and the field, but not on the Jacobian variety of the…

We improve a bound due to the second author on number of rational points on smooth surfaces in $\mathbb{P}^3$ over finite fields and look at families of surfaces that achieve or nearly achieve this bound, for which we compute their exact…

We classify all cubic extensions of any field of arbitrary characteristic, up to isomorphism, via an explicit construction involving three fundamental types of cubic forms. We deduce a classification of any Galois cubic extension of a…

The first part of this paper is devoted to an analysis of moment problems in R^n with supports contained in a closed set defined by finitely many polynomial inequalities. The second part of the paper uses the representation results of…

In this paper we first obtain the genus field of a finite abelian non-Kummer $l$--extension of a global rational function field. Then, using that the genus field of a composite of two abelian extensions of a global rational function field…

The $\beta\gamma$ system is generalized by complex(rational) powers of the fields, which leads to a corresponding extension on the Fock space. Two different approaches to compute the Green functions of the physical operators are proposed.…

Motivated by the intermediate Lang conjectures on hyperbolicity and rational points, we prove new finiteness results for non-constant morphisms from a fixed variety to a fixed variety defined over a number field by applying Faltings's…

We give asymptotic expressions for the number of commuting matrices over finite fields. For this, we use product expansions for the corresponding generating functions.