Related papers: Averages of multiplicative functions along equidis…
Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…
We give a completely elementary study for averages of short correlations of so-called sieve functions (a pretty general class of arithmetic functions).
We give a method for computing the ensemble average of multiplicative class functions over the Gaussian ensemble of real asymmetric matrices. These averages are expressed in terms of the Pfaffian of Gram-like antisymmetric matrices formed…
This paper gives upper and lower bounds on the gap in Jensen's inequality, i.e., the difference between the expected value of a function of a random variable and the value of the function at the expected value of the random variable. The…
We show that a wide variety of generalized increasing subsequence problems admit a one parameter family of extensions for which we can exactly compute the mean length of the longest increasing subsequence. By the nature of the extension,…
A multiplicative stochastic process with the lower bound lognormally distributed is investigated. For the process, the model is constructed, and its distribution function (involving four parameters) and the related statistical properties…
For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper…
A review of the state of the art of the comparison between any two different modes of convergence of sequences of measurable functions is carried out with focus on the algebraic structure of the families under analysis. As a complement of…
We prove an intermediate value theorem of an arithmetical flavor, involving the consecutive averages of sequences with terms in a given finite set A. For every such set we completely characterize the numbers x ("intermediate values") with…
We use some properties of orthogonal polynomials to provide a class of upper/lower variance bounds for a function $g(X)$ of an absolutely continuous random variable $X$, in terms of the derivatives of $g$ up to some order. The new bounds…
A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions for which the equality holds. We apply…
We study arithmetic inequalities for multiplicative, sub(super)-multiplicative, sub(super)-homogeneous functions. Applications for the classical arithmetic functions are pointed out.
An infinite family of Boolean polynomials which correspond to the discrete average maps, defined in [2], is constructed and their algebraic and combinatorial properties are investigated. They turn out to be balanced, and some recurrence…
We investigate the set of limit points of averages of rearrangements of a given sequence. We study how the properties of the sequence determine the structure of that set and what type of sets we can expect as the set of such accessible…
We generalize results of Jones and Olsen on multi-parameter moving ergodic averages to measure-preserving actions of $\mathbb R^d$ for $d\geq 1$. In particular, we give necessary and sufficient conditions for the pointwise convergence of…
We extend the Matom\"{a}ki-Radziwi\l\l{} theorem to a large collection of unbounded multiplicative functions that are uniformly bounded, but not necessarily bounded by 1, on the primes. Our result allows us to estimate averages of such a…
We evaluate friable averages of arithmetic functions whose Dirichlet series is analytically close to some negative power of the Riemann zeta function. We obtain asymptotic expansions resembling those provided by the Selberg-Delange method…
We study sums with multiplicative functions that take values over a non-homogenous Beatty sequence. We then apply our result in a few special cases to obtain asymptotic formulas such as the number of integers in a Beatty sequence…
An inequality for the variance of an additive function defined on random decomposable structures, called assemblies, is established. The result generalizes estimates obtained earlier in the cases of permutations and mappings of a finite set…
We obtain optimal lower bounds for moments of theta functions. On the other hand, we also get new upper bounds on individual theta values and moments of theta functions on average over primes. The upper bounds are based on bounds of…