Related papers: Genus fields of global fields

This is an exposition of some basic ideas in the realm of Global Inverse Function theorems. We address ourselves mainly to readers who are interested in the applications to Differential Equations. But we do not deal with those applications…

The reductions of conformal field theories which lead to generalized abelian cosets are studied. Primary fields and correlation functions of arbitrary abelian coset conformal field theory are explicitly expressed in terms of those of the…

Using a remainder theorem for valuations of a field, we give a new perspective on the norm function of a global field. We define the Euler totient function of a global field and recover the essential analytical properties of the classical…

We study generalized means whose domain may contain unbounded sets as well. We investigate usual properties of this type of means and also new attributes that regard for such means only. We examine how a mean defined on bounded sets can be…

For polynomials of degree two over finite fields, we present an improvement of Fitzgerald's characterization (Finite Fields Appl. 9(1):117-121, 2003). We then use this new characterization to obtain an explicit, complete, and simple…

We call a (q-1)-th Kummer extension of a cyclotomic function field a quasi-cyclotomic function field if it is Galois, but non-abelian, over the rational function field with the constant field of q elements. In this paper, we determine the…

We give a definition of a class of Dedekind domains which includes the rings of integers of global fields and give a proof that all rings in this class have finite ideal class group. We also prove that this class coincides with the class of…

This note describes some open problems that can be examined with the purpose of gaining additional insight of how to solve the problem of finding a general classification of geodetic graphs

We construct a generalised formalism for group field theories, in which the domain of the field is extended to include additional proper time variables, as well as their conjugate mass variables. This formalism allows for different types of…

We develop a notion of (principal) differential rank for differential-valued fields, in analog of the exponential rank and of the difference rank. We give several characterizations of this rank. We then give a method to define a derivation…

We present new classes of permutation polynomials over finite fields.

Given a totally real number field $F$, we show that there are only finitely many totally real extensions of $K$ of a fixed degree that admit a universal quadratic form defined over $F$. We further obtain several explicit classification…

Planar functions are special functions from a finite field to itself that give rise to finite projective planes and other combinatorial objects. We consider polynomials over a finite field $K$ that induce planar functions on infinitely many…

We present a novel approach to generic programming over extensible data types. Row types capture the structure of records and variants, and can be used to express record and variant subtyping, record extension, and modular composition of…

We study the structure of an algebraically closed field with extra function resembling the classical exponentiation on complex numbers.

We use cell decomposition techniques to study additive reducts of p- adic fields. We consider a very general class of fields, including fields with infinite residue fields, which we study using a multi-sorted language. The results are used…

The space of derivations of finite dimensional evolution algebras associated to graphs over a field with characteristic zero has been completely characterized in the literature. In this work we generalize that characterization by describing…

We study the correspondence between four-dimensional supersymmetric gauge theories and two-dimensional conformal field theories in the case of N=2* gauge theory. We emphasize the genus expansion on the gauge theory side, as obtained via…

We determine the zeta functions of trinomial curves in terms of Gauss sums and Jacobi sums, and we obtain an explicit formula of the genus of a trinomial curve over a finite field, then we study the conditions for a trinomial curve to be a…

Group field theories are particular quantum field theories defined on D copies of a group which reproduce spin foam amplitudes on a space-time of dimension D. In these lecture notes, we present the general construction of group field…