Related papers: Pseudofinite fields with additive and multiplicati…
We develop Kummer theory for algebraic function fields in finitely many transcendental variables. We consider any finitely generated Kummer extension (possibly, over a cyclotomic extension) of an algebraic function field, and describe the…
We introduce a model-complete theory which completely axiomatizes the structure $Z_{\alpha}=(Z, +, 0, 1, f)$ where $f : x \to \lfloor{\alpha} x \rfloor $ is a unary function with $\alpha$ a fixed transcendental number. When $\alpha$ is…
In this paper we consider estimating the number of solutions to multiplicative equations in finite fields when the variables run through certain sets with high additive structure. In particular, we consider estimating the multiplicative…
The theory of almost characters which is closely related to character sheaves is proposed by Lusztig to study the representation theory of finite reductive groups. In this article we show that the decomposition of the Weil character for…
According to the math tea argument, there must be real numbers that we cannot describe or define, because there are uncountably many real numbers, but only countably many definitions. And yet, the existence of pointwise-definable models of…
We prove that the (elementary) class of differential-difference fields in characteristic $p>0$ admits a model-companion. In the terminology of Chatzidakis-Pillay, this says that the class of differentially closed fields of characteristic…
We study various aspects of parafermionic theories such as the precise field content, a description of a basis of states (that is, the counting of independent states in a freely generated highest-weight module) and the explicit expression…
Assuming a certain form of resolution of singularities, we prove a general existential Ax-Kochen/Ershov principle for tamely ramified fields in all characteristics. This specializes to well-known results in residue characteristic $0$ and…
Let us consider a generalized Artin-Schreier algebraic function field extension $F$ of the rational function field $\F_{p^n}(x)$ defined over the finite field extension $K=\F_{p^n}$ of the prime field $\F_p$. We assume that $K$ is…
The goal of the present paper is to characterize the norm and quasi-norm forms defined over an arbitrary number field F in terms of their values at the S-integer points, where S is a finite set of valuations of F containing the archimedean…
We introduce a regularized free energy $\mathcal{F}_{\text{AdS}}$ for massive quantum field theories (QFTs) on Anti-de Sitter space (AdS). We conjecture this quantity to be monotonic under the renormalization group (RG) flow induced by…
A mathematics student's first introduction to the fundamental theorem of finite fields (FTFF) often occurs in an advanced abstract algebra course and invokes the power of Galois theory to prove it. Yet the combinatorial and algebraic coding…
Numerous results on self-reciprocal polynomials over finite fields have been studied. In this paper we generalize some of these to a-self reciprocal polynomials defined in [4]. We consider some properties of the divisibility of a-reciprocal…
We show that any countable model of a model complete theory has an elementary extension with a "pseudofinite-like" quasidimension that detects dividing.
In this paper we study the asymptotic theory for spectral analysis of stationary random fields, including linear and nonlinear fields. Asymptotic properties of Fourier coefficients and periodograms, including limiting distributions of…
In this paper we prove some results on the possible multiplicative orders of $\alpha + \alpha^{-1}$ when $\alpha$ is a non-zero element of a finite field of characteristic 2. The results of the paper rely on a previous investigation on the…
We present an extension to the quantifier-free theory of integer arrays which allows us to express counting. The properties expressible in Array Folds Logic (AFL) include statements such as "the first array cell contains the array length,"…
The aim of this work is to analyze general infinite sums containing modified Bessel functions of the second kind. In particular we present a method for the construction of a proper asymptotic expansion for such series valid when one of the…
We examine statistical field theories of polymeric fluids in view of performing numerical simulations. The partition function of these systems can be expressed as a functional integral over real density fields. The introduction of density…
We investigate certain arithmetic properties of field theories. In particular, we study the vacuum structure of supersymmetric gauge theories as algebraic varieties over number fields of finite characteristic. Parallel to the Plethystic…