Related papers: A Totient Function Inequality
Motivated by an application of semigroup variants to the discrete log problem in groups and related cryptographic applications, we introduce a new kind of totient function, related to both Euler's function and a generalisation of Euler's…
In this note we deal with some inequalities for the tangent function that are valid for $x$ in $(-\pi/2,\pi/2)$. These inequalities are optimal in the sense that the best values of the exponents involved are obtained.
In this paper, by using a general result on the monotonicity of quotients of power series, our aim is to prove some monotonicity and convexity results for the modified Struve functions. Moreover, as consequences of the above mentioned…
We offer new Tauberian theorems for a generalized partition function as our main result. Our analysis provides insight into asymptotic behavior of power series with arithmetic functions as coefficients.
The classical Gaussian concentration inequality for Lipschitz functions is adapted to a setting where the classical assumptions (i.e. Lipschitz and Gaussian) are not met. The theory is more direct than much of the existing theory designed…
In this paper we are concerned with a Gordan-type theorem involving an arbitrary number of inequality functions. We not only state its validity under a weak convexity assumption on the functions, but also show it is an optimal result. We…
This paper sketches the history of the Takagi function T and surveys known properties of T, including its nowhere-differentiability, modulus of continuity, graphical properties and level sets. Several generalizations of the Takagi function,…
The discrete Fourier transform of the greatest common divisor is a multiplicative function, if taken with respect to the same order of the primitive root of unity, which is a well known fact. As such, the transform can be expressed in the…
We introduce and consider a certain probability question involving elementary number theory and the likelihood that a fixed prime will appear in a certain recursively defined factorization of an integer. We derive several convergent…
In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…
Using elementary methods we find surprising connections between the values of the Riemann Zeta Function over integers and the fractional parts of rational powers, and a connection between the Riemann Zeta Function and the Prime Zeta…
A broad set of sufficient conditions that guarantees the existence of the maximum entropy (maxent) distribution consistent with specified bounds on certain generalized moments is derived. Most results in the literature are either focused on…
The Wigner functions on the one dimensional lattice are studied. Contrary to the previous claim in literature, Wigner functions exist on the lattice with any number of sites, whether it is even or odd. There are infinitely many solutions…
In this paper, we establish the irrationality of some open problems in mathematics based on using a recursive formula that generate the complete sequence of numbers. see [1] But before getting into that we begin with some Ramanujan notable…
This article offers different proofs of ten inequalities from those already published. So that the readers can see for themselves, the tasks specified in the condition of the source and classical inequalities which used in previously…
This paper provides a new and more direct proof of the assertion that a Turing computable function of the natural numbers is primitive recursive if and only if the time complexity of the corresponding Turing machine is bounded by a…
The prime number problem falls within the realm of number theory, specifically elementary number theory. Current research approaches have unnecessarily complicated this matter. In contrast to more advanced mathematical tools, the methods of…
In this paper we discuss mechanical systems with inequality constraints. We demonstrate how such constraints can be taken into account by proper modification of the action which describes the original unconstrained dynamics. To illustrate…
For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…