Stein's method is applied to obtain a general Cramér-type moderate deviation result for
dependent random variables whose dependence is defined in terms of a Stein identity. A …

Divide-and-conquer recurrences of the form f (n)= f (⌊ n/2⌋)+ f (⌈ n/2⌉)+ g (n)(n⩾ 2), with g
(n) and f (1) given, appear very frequently in the analysis of computer algorithms and related …

Among all sequences that satisfy a divide-and-conquer recurrence, those which are rational
with respect to a numeration system are certainly the most basic and the most essential …

Generalized Zeckendorf decompositions are expansions of integers as sums of elements of
solutions to recurrence relations. The simplest cases are base-b expansions, and the …

Abstract The sums $ S_ {q}(N) $ are defined by the equality $ S_ {q}(N)= s_q (1)+\dots+ s_q
(N-1) $ for all positive integers $ N $ and $ q\geqslant2 $, where $ s_q (n) $ is the sum of …

Let G¯ n=∏ k= 0 nnk, the product of the elements of the n th row of Pascal's triangle. This
paper studies the partial factorizations of G¯ n given by the product G (n, x) of all prime …

This paper studies an integer sequence $\overline {G} _n $ analogous to the product $
G_n=\prod_ {k= 0}^ n\binom {n}{k} $, the product of the elements of the $ n $-th row of …

This dissertation treats three topics in number theory. The first topic concerns the problem of
determining the optimal constant in the Montgomery–Vaughan weighted generalization of …

In this paper we study correlation measures introduced in\cite {emme_asymptotic_2017}.
Denote by $\mu_a (d) $ the asymptotic density of the set $\mathcal {E} _ {a, d}=\{n\in\mathbb …

A measure theoretic approach to study the power and the exponential sums for the usual
coding system has been developed since the 1990s. In this paper, we first introduce a new …