Related papers: An ordinary cyclotomic function field

For $p$ prime, let $\mathcal{H}^n$ be the linear span of characteristic functions of hyperplanes in $(\mathbb{Z}/p^k\mathbb{Z})^n$. We establish new upper bounds on the dimension of $\mathcal{H}^n$ over $\mathbb{Z}/p\mathbb{Z}$, or…

In this paper, we introduced the concept of a $p$-ideal for a given ring. We provide necessary and sufficient condition for $\dfrac{R[x]}{(f(x))}$ to be a $p$-ring, where $R$ is a finite $p$-ring. It is also shown that the amalgamation of…

A generic method to construct zero-difference functions (ZDFs) on algebraic rings is proposed in this paper. Then this method is used over some rings $\mathbb{Z}_{p^k}$, where $p$ is a prime number and $k\ge 2$ is a positive integer, and…

We give a new definition of a $p$-adic $L$-function for a mixed signature character of a real quadratic field and for a nontrivial ray class character of an imaginary quadratic field. We then state a $p$-adic Stark conjecture for this…

In this paper, we define a new subclass of $k$-uniformly starlike functions of order $\gamma,\ (0\leq\gamma<1)$ by using certain generalized $q$-integral operator. We explore geometric interpretation of the functions in this class by…

It is well known that for any finite Galois extension field $K/F$, with Galois group $G = \mathrm{Gal}(K/F)$, there exists an element $\alpha \in K$ whose orbit $G\cdot\alpha$ forms an $F$-basis of $K$. Such an element $\alpha$ is called…

Let ${\{K_m\}_{m\geq 4}}$ be the family of non-normal totally real cubic number fields defined by the irreducible cubic polynomial $f_m(x)=x^3-mx^2-(m+1)x-1$, where $m$ is an integer with $m\geq 4$. In this paper, we will give a class…

We give a description of the category of ordinary K3 surfaces over a finite field in terms of linear algebra data over Z. This gives an analogue for K3 surfaces of Deligne's description of the category of ordinary abelian varieties over a…

We give a bound of $k$ for a very ample lattice polytope to be $k$-normal. Equivalently, we give a new combinatorial bound for the Castelnuovo-Mumford regularity of normal projective toric varieties.

Let f(x) be a polynomial of degree at least 5 with complex coefficients and without repeated roots. Let p be an odd prime. Suppose that all the coefficients of f(x) lie in a subfield K such that: 1) K contains a primitive p-th root of…

Let $\mathcal{V}$ be a complete discrete valued ring of mixed characteristic $(0,p)$, $K$ its field of fractions, $k$ its residue field which is supposed to be perfect. Let $X$ be a separated $k$-scheme of finite type and $Y$ be an open…

Let $F$ be a number field, $k$ a positive integer. In this paper, we define the Mobius and Liouville functions of order $k$ in $F$. We give a formula about the partial sums of them by using elementary number theory and complex analysis.…

We show that spaces of Colombeau generalized functions with smooth parameter dependence are isomorphic to those with continuous parametrization. Based on this result we initiate a systematic study of algebraic properties of the ring…

We study the regularity of the distance function to the boundary of a domain in $\mathbb{R}^n$, with respect to the Minkowski functional of a convex polytope. We obtain the regularity of the distance function in certain cases. We also…

Let p be an odd prime. Let K_p = \Q(zeta_p) be the p-cyclotomic field. We apply a Kummer and Stickelberger relation of K_p to some singular not primary numbers A of K_p connected to p-class group of K_p and prove they verify the congruence…

In this article we consider functions $f$ meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions. This condition simplifies and generalizes known conditions. We…

Let $ \mathcal{S}(p) $ be the class of all meromorphic univalent functions defined in the unit disc $ \mathbb{D} $ of the complex plane with a simple pole at $ z=p $ and normalized by the conditions $ f(0)=0 $ and $ f^{\prime}(0)=1 $. In…

The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. Here we explore some natural properties in the context of excellent, equidimensional rings containing a field. In addition, we…

In this article we study the field of rational constants and Darboux polynomials of a generalized cyclotomic $K$-derivation $d$ of $K[X]$. It is shown that $d$ is without Darboux polynomials if and only if $K(X)^d=K$. Result is also studied…

For a rational function f we consider the norm of the derivative with respect to the spherical metric and denote by K(f) the supremum of this norm. We give estimates of this quantity K(f) both for an individual function and for sequences of…