Related papers: Integration on valuation fields over local fields
The article is devoted to stochastic processes with values in finite-dimensional vector spaces over infinite locally compact fields with non-trivial non-archimedean valuations. Infinitely divisible distributions are investigated. Theorems…
Partial zeta functions of algebraic varieties over finite fields generalize the classical zeta function by allowing each variable to be defined over a possibly different extension field of a fixed finite field. Due to this extra variation…
We identify a partition-theoretic generalization of Riemann zeta function and the equally positive integer-indexed harmonic sums at infinity, to obtain the generating function and the integral representations of the latter. The special…
In this note, we show that the values of integrals of the log-tangent function with respect to any square-integrable function on $\left[0 , \frac{\pi}{2} \right]$ may be determined by a finite or infinite sum involving the Riemann…
In this paper, we undertake a systematic model and valuation theoretic study of the class of ordered fields which are dense in their real closure. We apply this study to determine definable henselian valuations on ordered fields, in the…
We reformulate gauge theories in analogy with the vierbein formalism of general relativity. More specifically, we reformulate gauge theories such that their gauge dynamical degrees of freedom are local fields that transform linearly under…
We give a characterization, in terms of the residue field, of those henselian valuation rings and those henselian valuation ideals that are diophantine. This characterization gives a common generalization of all the positive and negative…
A brief introduction to Topological Quantum Field Theory as well as a description of recent progress made in the field is presented. I concentrate mainly on the connection between Chern-Simons gauge theory and Vassiliev invariants, and…
We present a unifying theory of fields with certain classes of analytic functions, called fields with analytic structure. Both real closed fields and Henselian valued fields are considered. For real closed fields with analytic structure,…
Explicit expressions for the expectation values and the variances of some observables, which are bilinear quantities in the quantum fields on a D-dimensional manifold, are derived making use of zeta function regularization. It is found that…
An efficient evaluation method is described for polynomials in finite fields. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large enough. Applications to the syndrome computation…
This work is a survey of relations between Drinfeld modules and higher dimensional fields of positive characteristic. The main new result stated is the expression of vanishing orders of certain modular forms through partial zeta values.
We continue the work of Kaplansky on immediate valued field extensions and determine special properties of elements in such extensions. In particular, we are interested in the question when an immediate valued function field of…
Higher-rank Minkowski valuations are efficient means for describing the geometry and connectivity of spatial patterns. We show how to extend the framework of the scalar Minkowski valuations to vector- and tensor-valued measures. The…
We introduce the notion of a field of covariances, a contravariant functor from non-commutative probability spaces to Hilbert spaces, as the natural categorical analogue of statistical covariance. In the case of finite-dimensional…
We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of…
We provide the construction of a set of square matrices whose translates and rotates provide a Parseval frame that is optimal for approximating a given dataset of images. Our approach is based on abstract harmonic analysis techniques.…
A method to regularize and renormalize the fluctuations of a quantum field in a curved background in the $\zeta$-function approach is presented. The method produces finite quantities directly and finite scale-parametrized counterterms at…
A new integral representation of smooth translation invariant and rotation equivariant even Minkowski valuations is established. Explicit formulas relating previously obtained descriptions of such valuations with the new more accessible one…
We investigate the integrability of polynomial vector fields through the lens of duality in parameter spaces. We examine formal power series solutions annihilated by differential operators and explore the properties of the integrability…