Related papers: Expansions in completions of global function field…
Let $(K, v)$ be a Henselian discrete valued field with a quasifinite residue field. This paper proves the existence of an algebraic extension $E/K$ satisfying the following: (i) $E$ has dimension dim$(E) \le 1$, i.e. the Brauer group Br$(E…
In this work we present some arithmetic properties of families of abelian $p$--extensions of global function fields, among which are their generators and their type of ramification and decomposition.
We undertake a study of extensions of unirational algebraic groups. We prove that extensions of unirational groups are also unirational over fields of degree of imperfection $1$, but that this fails over every field of higher degree of…
In this short note we confirm the relation between the generalized $abc$-conjecture and the $p$-rationality of number fields. Namely, we prove that given K$/\mathbb{Q}$ a real quadratic extension or an imaginary $S_3$-extension, if the…
In the paper, we shall establish the existence of a meromorphic continuation of the Global Zeta Function $\zeta(f,\chi)$ of a Global Number Field $K$ and also deduce the functional equation for the same, using different properties of the…
In this paper we study the description of the functional graphs associated with the power maps over finite groups. We present a structural result which describes the isomorphism class of these graphs for abelian groups and also for flower…
In 2007, Jarden and Narkiewicz raised the following question: Is it true that each algebraic number field has a finite extension L such that the ring of integers of L is generated by its units (as a ring)? In this article, we answer the…
The paper gives some criteria for partial sums of rational number sequences to be not rational functions and to be not algebraic functions. As an application, we study partial sums of some famous rational number sequences in mathematical…
For a fairly general class of two-dimensional tiling substitutions, we prove that if the length expansion $\beta$ is a Pisot number, then the tilings defined by the substitution must be locally finite. We also give a simple example of a…
A recent refinement of Ker\'ekj\'art\'o's Theorem has shown that in $\mathbb R$ and $\mathbb R^2$ all $\mathcal C^l$-solutions of the functional equation $f^n =\textrm{Id}$ are $\mathcal C^l$-linearizable, where $l\in \{0,1,\dots \infty\}$.…
The number of points on a certain one parameter family of algebraic surface over a finite field $\F_p$ can be expressed as $p^2+A_p(\lambda),$ where $A_p(\lambda)$ is a character sum and $\lambda$ is an element of the finite field $\F_p.$…
The problem of extending derivations of a field $F$ to an $F-$algebra $B$ is widely studied in commutative algebra and non-commutative ring theory. For example, every derivation of $F$ extends to $B$ if $B$ is a separable algebraic…
We study asymptotics of integrals of certain rational functions that depend on parameters in a field $K$ of characteristic zero. We use formal power series to represent the integral and prove certain identities about its coefficients…
Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.
Based on a canonical approach and functional-integration techniques, a series expansion of Green's function of a scalar field, in the presence of a medium, is obtained. A series expansion for Lifshitz-energy, in finite-temperature, in terms…
The study of solutions to polynomial equations over finite fields has a long history in mathematics and is an interesting area of contemporary research. In recent years the subject has found important applications in the modelling of…
For finite extensions of a rational function field over a finite field, we prove a "P-adic class formula" in the spirit Taelman's work.
There is proposed the Maillet--Malgrange type theorem for a generalized power series (having complex power exponents) formally satisfying an algebraic ordinary differential equation. The theorem describes the growth of the series…
We address the question of computing one selected term of an algebraic power series. In characteristic zero, the best algorithm currently known for computing the $N$th coefficient of an algebraic series uses differential equations and has…
We show that the iterative logarithm of each non-linear entire function is differentially transcendental over the ring of entire functions, and we give a sufficient criterion for such an iterative logarithm to be differentially…