Related papers: A note on Sonnenschein summability matrices
In this article a new method of generating sums of like powers is presented.
Sum of powers 1^p+...+n^p, with n and p being natural numbers and n>=1, can be expressed as a polynomial function of n of degree p+1. Such representations are often called Faulhaber formulae. A simple recursive algorithm for computing…
We study analogues of classical inequalities for the eigenvalues of sums of pseudo-Hermitian matrices.
This paper provides a technique for evaluating some nonlinear Gaussian sums in closed forms. The evaluation is obtained from the known values of simpler exponential sums.
In this note, we presented a new decomposition of elements of finite fields of even order and illustrated that it is an effective tool in evaluation of some specific exponential sums over finite fields, the explicit value of some…
We prove an explicit formula to count the partitions of $n$ whose product of the summands is at most $n$. In the process, we also deduce a result to count the multiplicative partitions of $n$.
We define two notions of partial sums of a Riordan array, corresponding respectively to the partial sums of the rows and the partial sums of the columns of the Riordan array in question. We characterize the matrices that arise from these…
Perturbative calculations in field theory at finite temperature involve sums over the Matsubara frequencies. Besides the usual difficulties that appear in perturbative computations, these sums give rise to some new obstacles that are…
In this paper, we study sum formulas for Schur multiple zeta values and give a generalization of the sum formulas for multiple zeta(-star) values. We show that for ribbons of certain types, the sum over all admissible Young tableaux of this…
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment…
In this paper we consider Dedekind type DC sums and prove receprocity laws related to DC sums.
We describe a method to compute Hurwitz-Hodge integrals.
The article presents a generalization of Sherman-Morrison-Woodbury (SMW) formula for the inversion of a matrix of the form A+sum(U)k)*V(k),k=1..N).
We present a method for calculating any (nested) harmonic sum to arbitrary accuracy for all complex values of the argument. The method utilizes the relation between harmonic sums and (derivatives of) Hurwitz zeta functions, which allows a…
By simple elementary method,we obtain with ease,a highly simple expression for the remainder term of the divisor problem and use it to obtain an Euler-Maclaurin analogue of summation involving divisor function.We also obtain a relation…
The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…
In this short note we present a class of conjectures on partitions of integers as summations of primes, which are extensions of Goldbach conjecture.
This is a short introduction to Weingarten Calculus. Weingarten Calculus is a method to compute the joint moments of matrix variables distributed according to the Haar measure of compact groups.
The main result of the note describes certain optimal-score partitions, which can be interpreted as optimal resource allocations. This result is based on the fact that any nonnegative square matrix whose column sums are the same as the…