Related papers: About Eisenstein's Theorem
We review the status of "Einstein-Aether theory", a generally covariant theory of gravity coupled to a dynamical, unit timelike vector field that breaks local Lorentz symmetry. Aspects of waves, stars, black holes, and cosmology are…
In this note, we study substructures of generalised power series fields induced by families of well-ordered subsets of the group of exponents. We characterise the set-theoretic and algebraic properties of the induced substructures in terms…
In an earlier preprint (math.AG/9810142) we gave an explicit description of the algebraic closure of the field of power series over a field of characteristic p, in terms of "generalized power series". In this paper, we give an analogous…
This paper explores the ER bridges theory and its relationship with quantum phenomena. An argument can be made that the ER bridges theory does not explicitly address quantum phenomena and implies that Einstein intended to differentiate…
The purpose of this article is to highlight the fascinating, but only very incompletely understood relation between Einstein's theory and its generalizations on the one hand, and the theory of indefinite, and in particular hyperbolic, Kac…
The aim of this paper is to generalize a main theorem concerning weighted mean summability to absolute matrix summability which plays a vital role in summability theory and applications to the other sciences by using quasi-$f$-power…
In this paper we compute the density of monic and non-monic Eisenstein polynomials of fixed degree having entries in an integrally closed subring of a function field over a finite field.
We review some topics in the analytic theory of Eisenstein series, including meromorphic continuation, $L^2$-spectral expansion and Fourier coefficients. We also discuss some open problems.
The purpose of this article is to provide an exposition of domains of convergence of power series of several complex variables without recourse to relatively advanced notions of convexity.
The main aim of the paper is to prove a fountain theorem without assuming the $\tau$-upper semicontinuity condition on the variational functional. Using this improved fountain theorem, we may deal with more general strongly indefinite…
At first a type of Eisenstein series is defined as distributions giving nearly-holomorphic automorphic forms on a totally real field, with different expressions (integral, summation) ; then these are shown to satisfied the expected…
We discuss the relevance of Eisenstein series for representing certain G(Z)-invariant string theory amplitudes which receive corrections from BPS states only. The Eisenstein series are constructed using G(Z)-invariant mass formulae and are…
We define the resultant of two power series with coefficients in the ring of integers of a $p$-adic field. In order to do this, we prove a universal version of the Weierstrass preparation theorem.
This article investigates a new gauge theoretic approach to Einstein's equations in dimension 4. Whilst aspects of the formalism are already explained in various places in the mathematics and physics literature, our first goal is to give a…
We study distribution of zeros of a complex polynomial whose coefficients has been modified. We give a new proof of the theorem of Rubinstein, and with similar method we prove a new theorem that is not generalization of the previous…
The interpretations of solutions of Einstein field's equations led to the prediction and the observation of physical phenomena which confirm the important role of general relativity, as well as other relativistic theories in physics. In…
The main aim of this work is to present the interpretation of the Ising type models as a kind of field theory in the framework of noncommutative geometry. We present the method and construct sample models of field theory on discrete spaces…
Eisenstein polynomials, which were defined by the second author, are analogues of the concept of an Eisenstein series. The second author conjectured that there exist some analogous properties between Eisenstein series and Eisenstein…
We study the physical effects of torsion as predicted by the Einstein-Cartan theory in the test particle approximation and the non-relativist limit. We first present the corresponding non-relativistic Hamiltonian for a 2-spinor. Then, we…
This survey presents an overview of the advances around Tverberg's theorem, focusing on the last two decades. We discuss the topological, linear-algebraic, and combinatorial aspects of Tverberg's theorem and its applications. The survey…