Related papers: About Eisenstein's Theorem
The aim of this work is to use the notions of Riemann's geometry introduced in Part I, to analyze the foundations of Einstein's theory of general relativity.
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…
There is proposed the Maillet--Malgrange type theorem for a generalized power series (having complex power exponents) formally satisfying an algebraic ordinary differential equation. The theorem describes the growth of the series…
The main purpose of the paper is to establish a closedness theorem over Henselian valued fields $K$ of equicharacteristic zero (not necessarily algebraically closed) with separated analytic structure. It says that every projection with a…
This papper aims to present and demonstrate Clifford's version for a generalization of Miquel's theorem with the use of Euclidean geometry arguments only.
This expository essay is aimed at introducing the Jones polynomial. We will see the encapsulation of the Jones polynomial, which will involve topics in functional analysis and geometrical topology; making this essay an interdisciplinary…
In Einstein's general relativity, with its nonlinear field equations, the discoveries and analyzes of various specific explicit solutions made a great impact on understanding many of the unforeseen features of the theory. Some solutions…
We give a simple proof of the Emch closing theorem by introducing a new invariant measure on the circle. Special cases of that measures are well-known and have been used in the literature to prove Poncelet's and Zigzag theorems. Some…
To present a survey on known results from the theory of transposed Poisson algebras, as well as to establish new results on this subject, are the main aims of the present paper. Furthermore, a list of open questions for future research is…
In measure theory, Steinhaus theorem is a result that deals with a property of the difference between two sets of positive measure. We give a simple elementary proof of the result.
We obtain a Bernstein theorem for special Lagrangian graphs in n-dimensional complex space for arbitrary n only assuming bounded slope, but no quantitative restriction.
We introduce a linearized version of group field theory. It can be viewed either as a group field theory over the additive group of a vector space or as an asymptotic expansion of any group field theory around the unit group element. We…
In this paper we present a new method to study Fourier coefficients of holomorphic and non-holomorphic Eisenstein series simultaneously.
In this paper we go on to discuss about Stanley's theorem in Integer partitions. We give two different versions for the proof of the generalization of Stanley's theorem illustrating different techniques that may be applied to profitably…
Let K be an algebraically closed field of characteristic p. We exhibit a counterexample against a theorem asserted in one of our earlier papers, which claims to characterize the integral closure of K((t)) within the field of…
The purpose of this note is twofold. First, we survey results on the construction of large class groups of number fields by specialization of finite covers of curves. Then we give examples of applications of these techniques.
This review summarizes Effective Field Theory techniques, which are the modern theoretical tools for exploiting the existence of hierarchies of scale in a physical problem. The general theoretical framework is described, and explicitly…
The aim of this work is to use Napoleon's Theorem in different regular polygons, and decide whether we can prove Napoleon's Theorem is only limited with triangles or it could be done in other regular polygons that can create regular…
We study sums over primes of trace functions of $\ell$-adic sheaves. Using an extension of our earlier results on algebraic twist of modular forms to the case of Eisenstein series and bounds for Type II sums based on similar applications of…
This paper develops a theory of polynomial maps from commutative semigroups to arbitrary groups and proves that it has desirable formal properties when the target group is locally nilpotent. We apply this theory to solve Waring's Problem…