Related papers: A product representation of pi
In this short note we give an expression for some numbers $n$ such that the polynomial $x^{2p}-nx^p+1$ is reducible.
The aim of this short note is to show how can be derived from the properties of fundamental interpolation polynomials some nice identities.
Let $X$ be a normal algebraic variety over a finitely generated field $k$ of characteristic zero, and let $\ell$ be a prime. Say that a continuous $\ell$-adic representation $\rho$ of $\pi_1^{\text{\'et}}(X_{\bar k})$ is arithmetic if there…
The f-invariant is a higher version of the e-invariant that takes values in the divided congruences between modular forms; in the situation of a cartesian product of two framed manifolds, the f-invariant can actually be computed from the…
In this paper we evaluate sums and integrals of products of Fubini polynomials and have new explicit formulas for Fubini polynomials and numbers. As a consequence of these results new explicit formulas for p-Bernoulli numbers and…
This short note provides a sharper upper bound of a well known inequality for the sum of divisors function. This is a problem in pure mathematics related to the distribution of prime numbers. Furthermore, the technique is completely…
We relate a previous result of ours on families of Diophantine equations having only trivial solutions with a result on the approximation of an algebraic number by products of rational numbers and units. We compare this approximation with a…
By means of a modified hypervirial theorem we derive simple expressions for the integrals of products of Airy functions. Present results contain earlier ones as particular cases.
A little general abstract combinatorial nonsense delivered in this note is a presentation of some old and basic concepts, central to discrete mathematics, in terms of new words. The treatment is from a structural and systematic point of…
Purpose of writing this paper is to solve a transcendental function containing a product of a variable and its double exponential by a unique method of approximation. If the value of the said product is given, then its inverse function is…
Exclusive $\pi^o$ electroproduction from nucleons was first suggested by Ahmad, Goldstein and Liuti for extracting from experimental data the tensor charge, transversity and other quantities related to chiral odd combinations of generalized…
An elementary approach to the construction of Coxeter group representations is presented.
We produce a new, shorter construction of a minor-universal planar graph.
In this paper, we study the unit dot graph of product of commutative rings
An algorithm for computing /pi(N) is presented.It is shown that using a symmetry of natural numbers we can easily compute /pi(N).This method relies on the fact that counting the number of odd composites not exceeding N suffices to calculate…
We suggest a new approach to Artin's constant that leads to its representation as an infinite sum divided by another infinite sum. The same approach works well for Stephens' constant and higher rank Artin's constants. The main results are…
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…
In this note we introduce a representation of simple undirected graphs in terms of polynomials and obtain a unique code for a simple undirected graph.
The paper presents a counterexample to the Hodge conjecture.