相关论文: Examples of finite $p$-divisible sets of MHS

In this paper, we prove two results related to the solutions of norm form equations. Firstly, we give a finiteness result for sums of terms of linear recurrence sequences appearing in the coordinates of solutions of norm form equations.…

We show some new Wolstenholme type $q$-congruences for some classes of multiple $q$-harmonic sums of arbitrary depth with strings of indices composed of ones, twos and threes. Most of these results are $q$-extensions of the corresponding…

We study finite groups which possess a strongly p-embedded subgroup for some odd prime p. The main results of the paper will be applied in the ongoing project to classify the simple groups of local characteristic p.

The explicit formulas expressing harmonic sums via alternating Euler sums (colored multiple zeta values) are given, and some explicit evaluations are given as applications.

This paper extends classical results in the invariant theory of finite groups and finite group schemes to the actions of finite Hopf algebras on commutative rings.

These notes are devoted to the theory of exponential sums over finite fields. The first chapter recalls some of the number-theoretic interest of such sums. The second chapter discusses the $L$-functions attached to such sums, the "Weil…

This article examines the nontrivial solutions of the congruence \[ (p-1)\cdots(p-r) \equiv -1 \pmod p. \] We discuss heuristics for the proportion of primes $p$ that have exactly $N$ solutions to this congruence. We supply numerical…

This paper will give some examples of diffeomorphic complex 5-dimensional complete intersections and remarks on these examples. Then a result on the existence of diffeomorphic complete intersections that belong to components of the moduli…

This paper deals with (finite or infinite) sequences of arbitrary independent events in some probability space. We find sharp lower bounds for the probability of a union of such events when the sum of their probabilities is given. The…

We solve an elementary number theory problem on sums of fractional parts, using methods from group theory. We apply our result to deduce the finiteness of certain monodromy representations.

In this paper, we establish some fixed point theorems in ordered partial metric spaces. An example is given to illustrate our obtained results.

We prove that the coherent cohomology of a proper morphism of noetherian schemes can be made arbitrarily p-divisible by passage to proper covers (for a fixed prime p). Under some extra conditions, we also show that p-torsion can be killed…

An asymptotic formula for the number of partitions into p-cores is derived. As a byproduct some integer valued trigonometric sums are found

We give a criterion for an HNN extension of a finite $p$-group to be residually $p$.

Let $R$ be a commutative ring and $M$ a non-zero $R$-module. We introduce the class of \emph{pseudo strongly hollow submodules} (\emph{PS-hollow submodules}, for short) of $M$. Inspired by the theory of modules with \emph{secondary…

Here we consider piecewise fractional linear maps with three branches. The paper presents a study of invariant measures with densities which can be written as infinite series. These series either have infinitely many poles or they sum up to…

The objective of the paper is the study of Mneimneh-like sums with a parametric variant of the multiple harmonic-star values. We generalize and resolve the Pan-Xu conjecture on generalized Mneimneh-like sums and present their…

This is a survey of old and new problems and results in additive number theory.

In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.

In this paper we propose a conjecture concerning partial sums of an arbitrary finite subset of an abelian group, that naturally arises investigating simple Heffter systems. Then, we show its connection with related open problems and we…