Related papers: Moyennes effectives de fonctions multiplicatives c…
We unify in a large class of additive functions the results obtained in the first part of this work. The proof rests on series involving the Riemann zeta function and certain sums of primes which may have their own interest.
We estimate the average of any arithmetic function $k$ over the values of any smooth polynomial in many variables provided only that $k$ has a distribution in arithmetic progressions of fixed modulus. We give several applications of this…
Generalized integral formulas involving the generalized Bessel-Maitland function are considered and it expressed in terms of generalized Wright hypergeometric functions. By assuming appropriate values of the parameters in the main results,…
We introduce a new generalization of Stirling numbers of the second kind and analyze their properties, including generating functions, integral representations, and recurrence relations. These numbers are used to approximate Riemann zeta…
We prove mixed-norm estimates for circular averages with respect to $\alpha$-dimensional fractal measures on $\mathbb{R}^2$, using circle tangency bounds when $\alpha \in (0,1]$ and a $\delta$-discretized slicing lemma for fractals when…
Exact summatory functions that count the number of prime $k$-tuples up to some cut-off integer are presented. Related summatory $k$-tuple analogs of the first and second Chebyshev functions are then defined. Using a gamma distribution…
We establish an asymptotic formula for the logarithmic mean value of a 1-bounded multiplicative function that is sharp in many cases of interest. We derive from it a variety of applications, making progress on several old problems. As a…
In this paper, we first study the arithmetic properties of intuitionistic fuzzy number, the monotonicity of intuitionistic fuzzy function and the derivative of intuitionistic fuzzy functions and then we study the fundamental properties on…
We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…
In this paper, the Authors establish a new identity for differentiable functions. By the well-known H\"older and power mean inequality, they obtain some integral inequalities related to the convex functions and apply these inequalities to…
We consider stochastic versions of the Cauchy exponential functional equation and give a martingale characterization of the general solution.
Estimation of linear and quadratic functionals over different classes of univalent functions is one of the classical problems in geometric function theory. In this paper we solve the problem over some classes of so-called non-linear…
Using probability theory we derive an expression for the sum of a series of definite integrals involving upper incomplete Gamma functions. In the proof, a normal variance mixture distribution with Beta mixing distributions plays a crucial…
The definition of conservative-irreversible functions is extended to smooth manifolds. The local representation of these functions is studied and reveals that not each conservative-irreversible function is given by the weighted product of…
We study the distributional behavior of additive arithmetic functions evaluated at integers drawn from the harmonic distribution. Our main result shows that a broad family of such functions converges in law to conditioned Dickman-type…
We develop potential theory including a Bernstein-Walsh type estimate for functions of the form $p(z)q(f(z))$ where $p,q$ are polynomials and $f$ is holomorphic. Such functions arise in the study of certain ensembles of probability measures…
The main purpose of present paper is to determine some lower bounds for the quotient of the normalized hyper-Bessel function and its partial sum, as well as for the quotient of the derivative of normalized hyper-Bessel function and its…
We present some properties of the gradient of a mu-differentiable function. The Method of Lagrange Multipliers for mu-differentiable functions is then exemplified.
The simple product formulae for derivatives of scalar functions raised to different powers are generalized for functions which take values in the set of symmetric positive definite matrices. These formulae are fundamental in derivation of…
Mixture of experts (MoE) models are widely applied for conditional probability density estimation problems. We demonstrate the richness of the class of MoE models by proving denseness results in Lebesgue spaces, when inputs and outputs…