相关论文: Simple proof of Gallagher's singular series sum es…

We consider the series of reciprocals of those positive integers with exactly $k$ occurrences of a given $b$-ary digit $d$ (Irwin series), and obtain geometrically convergent representations for their sums. They are expressed in terms of…

In this short note, we obtain error estimates for Riemann sums of some singular functions.

In this paper, we study the Jacobi sums over Galois rings of arbitrary characteristics and completely determine their absolute values, which extends the work in \cite{feng1}, where the Jacobi sums over Galois rings with characteristics a…

A few elementary estimates of a basic character sum over the prime numbers are derived here. These estimates are nontrivial for character sums modulo large q. In addition, an omega result for character sums over the primes is also included.

In this paper, by providing the uniform gradient estimates for a sequence of the approximating equations, we prove the existence, uniqueness and regularity of the conical parabolic complex Monge-Amp\`ere equation with weak initial data. As…

A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.

We develop a cohomological method to classify amalgams of groups. We generalize this to simplicial amalgams in any concrete category. We compute the non-commutative 1-cohomology for several examples of amalgams defined over small simplices.

We studied two probabilistic models of the distribution of primes in the natural number [1].The paper considers the third probabilistic model of the distribution of primes in the natural number. The author proved that the results obtained…

Average of exponential ${\rm Tr}_R e^X$, i.e. of a group rather than an algebra character, in Gaussian matrix model is known to be an amusing generalization of Schur polynomial, where time variables are substituted by traces of products of…

It is proven an analogue of The Theorem of Moser according to an iterative normalization procedure depending on Generalized Fischer Decompositions.

We survey the classical results on the prime number theorem

In this paper, we consider universal sums of generalized polygonal numbers. Fixing $m\in\mathbb{N}_{\geq 3}$, we show two finiteness theorems for universal sums of generalized polygonal numbers whose inputs have a restricted number $L$ of…

Translation from the Latin original, "Inventio summae cuiusque seriei ex dato termino generali" (1735). E47 in the Enestrom index. In this paper Euler derives the Euler-Maclaurin summation formula, by expressing y(x-1) with the Taylor…

In this paper, we consider three families of numerical series with general terms containing the harmonic numbers, and we use simple methods from classical and complex analysis to find explicit formulas for their respective sums.

This is an announcement of conjectures and results concerning the generating series of Euler characteristics of Hilbert schemes of points on surfaces with simple (Kleinian) singularities. For a quotient surface C^2/G with G a finite…

The aim of this paper is to prove Cotlar's ergodic theorem modeled on the set of primes.

The formula for the calculation of the adjacency indices of types $D_\mu^\pm$ Legendrian monosingularities to multisingularities of types $A_{\mu_1}^{k_1}\dots A_{\mu_p}^{k_p}$ is obtained in the paper. Namely the number of strata of a…

In this article we prove an algebraic identity which significantly generalizes the formula for sum of powers of consecutive integers involving Stirling numbers of the second kind. Also we have obtained a generalization of Newton-Girard…

We prove some properties of the sequence $\{a_n\}_{n\ge1}$ defined by $a_n=\pi(n)-\pi\bigl(\textstyle\sum_{k=1}^{n-1}a_k\bigr).$

Let $X$ be a set of positive integers, and let $\mathbb Z_K$ be the ring of integers of a number field $K$ of degree $n$. Denote by $N(I)$ the absolute norm of an ideal $I$ of $\mathbb Z_K$, and by $\mathcal A$ the set of principal ideals…