Related papers: Fields, towers of function fields meeting asymptot…

Fix $K/\mathbf{Q}_p$ a finite extension and let $L/K$ be an infinite, strictly APF extension in the sense of Fontaine--Wintenberger. Let $X_K(L)$ denote its associated norm field. The goal of this paper is to associate to $L/K$, in a…

We extend coded distributed computing over finite fields to allow the number of workers to be larger than the field size. We give codes that work for fully general matrix multiplication and show that in this case we serendipitously have…

Let G be a compact Lie group. We build a tower of G-spectra over the suspension spectrum of the space of linear isometries from one G-representation to another. The stable cofibres of the maps running down the tower are certain interesting…

Given an algebraic variety defined over a discrete valuation field and a skeleton of its Berkovich analytification, the tropicalization process transforms function field of the variety to a semifield of tropical functions on the skeleton.…

Let $K/F$ be a quadratic tamely ramified extension of a non-Archimedean local field $F$ of characteristic zero. In this paper, we give an explicit formula for Langlands' lambda function $\lambda_{K/F}$.

In this paper, we will give an overview of known and new techniques on how one can obtain explicit equations for candidates of good towers of function fields. The techniques are founded in modular theory (both the classical modular theory…

We prove a Torelli-like theorem for higher-dimensional function fields, from the point of view of "almost-abelian" anabelian geometry.

Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…

Let $K$ be an algebraically closed field, and let $F/K(x)$ be a Kummer extension of function fields of genus $g$. We provide a compact and explicit description of the gap set $G(Q)$ at any totally ramified place $Q$ of the extension…

We answer various questions concerning the distribution of extensions of a given central simple algebra $K$ over a number field. Specifically, we give asymptotics for the count of inner Galois extensions $L/K$ of fixed degree and center…

Let K be an abelian extension of a totally real number field k, K^+ its maximal real subfield and G=Gal(K/k). We have previously used twisted zeta-functions to define a meromorphic CG-valued function Phi_{K/k}(s) in a way similar to the use…

We establish new conditions that prevent the existence of (weak) normal integral bases in tame Galois extensions of number fields. This leads to the following result: under appropriate technical hypotheses, the existence of a normal…

We give a general construction of correlation functions in rational conformal field theory on a possibly non-orientable surface with boundary in terms of 3-dimensional topological quantum field theory. The construction applies to any…

We generalise the Siegel-Voloch theorem about S-integral points on elliptic curves as follows: let K/F denote a global function field over a finite field F of characteristic p>3, let S denote a finite set of places of K and let E/K denote a…

Given a number field $K$ one associates to it the set $\Lambda_K$ of Dedekind zeta-functions of finite abelian extensions of $K$. In this short note we present a proof of the following Theorem: for any number field $K$ the set $\Lambda_K$…

In this note, we give a construction of codes on algebraic function field $F/ \mathbb{F}_{q}$ using places of $F$ (not necessarily of degree one) and trace functions from various extensions of $\mathbb{F}_{q}$. This is a generalization of…

Given a number field $k$, we show that, for many finite groups $G$, all the Galois extensions of $k$ with Galois group $G$ cannot be obtained by specializing any given finitely many Galois extensions $E/k(T)$ with Galois group $G$ and $E/k$…

Calculations in field theory are usually accomplished by employing some variants of perturbation theory, for instance using loop expansions. These calculations result in asymptotic series in powers of small coupling parameters, which as a…

For a finite group $G$ and a sufficiently large (but fixed) prime power $q$ coprime to $G$ we obtain asymptotics for the number of regular Galois extensions $L/ \mathbb{F}_q(t)$, with $\mathrm{Gal}(L/\mathbb{F}_q(t)) \cong G$, ramified at a…

In this paper we present an approach to study arithmetical properties of global function fields by working with Artin L-functions. In particular we recall and then extend a criteria of two function fields to be arithmetically equivalent in…