Related papers: Generalization of Romanoff's theorem
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.
A generalization of the quotient integral formula is presented and some of its properties are investigated. Also the relations between two function spaces related to the spacial homogeneous spaces are derived by using general quotient…
In this paper we study the variance of the Euler totient function (normalized to $\varphi(n)/n$) in the integers $\mathbb{Z}$ and in the polynomial ring $\mathbb{F}_q[T]$ over a finite field $\mathbb{F}_q$. It turns out that in…
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
In this article we present certain formulas involving arithmetical functions. In the first part we study properties of sums and product formulas for general type of arithmetic functions. In the second part we apply these formulas to the…
A quaternionic partial differential equation is shown to be a generalisation of the Riccati ordinary differential equation and its relationship with the Schrodinger equation is established. Various approaches to the problem of finding…
Using a remainder theorem for valuations of a field, we give a new perspective on the norm function of a global field. We define the Euler totient function of a global field and recover the essential analytical properties of the classical…
Gonek, Graham, and Lee have shown recently that the Riemann Hypothesis (RH) can be reformulated in terms of certain asymptotic estimates for twisted sums with von Mangoldt function $\Lambda$. Building on their ideas, for each…
We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin glasses, and maxima of random fields.
Romanov proved that a positive proportion of the integers have a representation as a sum of a prime and a power of an arbitrary fixed positive integer. Rieger proved the analogous result for number fields. We will determine an explicit…
We prove several extensions of the Erdos-Fuchs theorem.
We recover Reidemeister's theorem using smooth functions and transversality.
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
The basis of this work is a simple, extended corollary of Wilson's theorem. This corollary generates many more quotients than those already generated by Wilson's theorem, and it was of interest to derive how they relate to each other and…
Using Eulerian and Euler numbers, we establish congruences concerning sums involving harmonic numbers, tangent numbers and Genocchi numbers.
In this paper we obtain a generalization of some integral inequalities related to Chebyshev`s functional by using a generalized Katugampola fractional integral.
The article deals with the generalized Newton--Kantorovich method for solving operator equations with nondifferentiable operators in Banach spaces. The convergence theorem is proved by means of majorant scalar equations.
In this note we propose a generalization of the Laplace and Fourier transforms which we call symmetric Laplace transform. It combines both the advantages of the Fourier and Laplace transforms. We give the definition of this generalization,…
We use Taylor's formula with Lagrange remainder to make a modern adaptation of Poisson's proof of a version of the fundamental theorem of calculus in the case when the integral is defined by Euler sums, that is Riemann sums with left (or…
This paper introduces the target sum function along with its characteristics. The target sum function takes a list of integers and a specific target integer as input values and expresses the number of ways to obtain the target sum by either…