Related papers: Examples of finite $p$-divisible sets of MHS
\medskip\noindent\textbf{R\'esum\'e.} Soit $l$ un entier et $\ors=(s_1, \dots, s_l)$ une s\'equence d'entiers positifs. Dans ce document, nous \'etudierons les propri\'et\'es arithm\'etique de sommes harmoniques multiples $H(\ors; n)$, qui…
In this paper we will study the p-divisibility of partial sums of multiple zeta value series. In particular we provide some generalizations of the classical Wolstenholme's Theorem.
In this paper we investigate congruence relationships of particular finite generalized harmonic numbers sums. We suggest more transparent and simpler method to analyse these sums and present several additional results for certain special…
In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals
Several results about the union-closed sets conjecture are presented.
The duality is a fundamental property of the finite multiple harmonic sums (MHS). In this paper, we prove a duality result for certain generalizations of MHS which appear naturally as the differences of MHS. We also prove a formula for the…
This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically…
We consider a special class of binomial sums involving harmonic numbers and we prove three identities by using the elementary method of the partial fraction decomposition. Some applications to infinite series and congruences are given.
We prove that, for any prime number $p\geq 5$, the set of natural numbers $n$ such that $p\mid H_n$ is finite.
PhD thesis concerning cohomological finiteness conditions of infinite discrete groups. Much of the material in this thesis has also appeared in arXiv:1311.7629, arXiv:1310.6262, arXiv:1311.6156, and arXiv:1207.1597.
The alternating multiple harmonic sums are partial sums of the infinite series defining the Euler sums which are the alternating version of the multiple zeta value series. In this paper, we present some systematic structural results of the…
In this paper, we present a general framework for the derivation of interesting finite combinatorial sums starting with certain classes of polynomial identities. The sums that can be derived involve products of binomial coefficients and…
Provides a counterexample to a long standing conjecture of A. Adem regarding the behaviour of the integral cohomology of a p-group.
In this paper we derive characterizations of boundedness of the subsequences of partial sums with respect to Vilenkin system on the martingale Hardy spaces when $ 0<p<1 $. Moreover, we find necessary and sufficient conditions for the…
In a previous work (arXiv:2505.05574), a summation formula for harmonic Maass forms of polynomial growth was established. In this note, we use the theory of $L$-series of harmonic Maass forms to state and prove a summation formula for such…
We introduce a general definition of almost $p$-summing mappings and give several concrete examples of such mappings. Some known results are considerably generalized and we present various situations in which the space of almost $p$-summing…
We construct explicit examples of $p$-harmonic maps $u:\mathbb{R}^n \to \mathbb{R}^N$. These are more irregular than the previously known examples and thus provide new upper bounds for the regularity of $p$-harmonic maps, including the case…
In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.
We prove one decomposition theorem of complex Monge-Ampere measures of plurisubharmonic functions in connection with their pluripolar sets.
We present a concise method for deriving an explicit formula for $p$-adic multiple zeta values. The formula features a variant of multiple harmonic sums, termed binomial multiple harmonic sums.