Related papers: A generalization of the duality for multiple harmo…
In this note, we show that for any harmonic map into a non-compact symmetric space one can find naturally a "dual" harmonic map into a compact symmetric space which can be constructed from the same basic data (called "potentials" in the…
A mixed type dual to a nondifferentiable variational problem involving higher order derivative is formulated and duality results are proved under generalized invexity conditions. Special cases are generated from our results.
We describe the duality between different geometries which arises by considering the classical and quantum harmonic map problem. To appear in ``Essays on Mirror Manifolds II''.
We show that a duality formula for certain parametrized multiple series yields numerous relations among them. As a result, we obtain a new relation among extended multiple zeta values, which is an extension of Ohno's relation for multiple…
The finite and infinite harmonic sums form the general basis for the Mellin transforms of all individual functions $f_i(x)$ describing inclusive quantities such as coefficient and splitting functions which emerge in massless field theories.…
Two types of finite series of products of harmonic numbers involving nonnegative integer powers are evaluated, also yielding two other important harmonic number identities. The recursion formulas for these sums are derived, which are easily…
A multiple Gauss sum is a complete multiple exponential sum twisted by Dirichlet characters. We prove a new bound for multiple Gauss sums and, as an application, improve previous results in the Birch--Goldbach problem. Let $F_1, \ldots, F_R…
\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 mainly show that Euler sums of generalized hyperharmonic numbers can be expressed in terms of linear combinations of the classical Euler sums.
Recently, Maesaka, Seki and Watanabe discovered a surprising equality between multiple harmonic sums and certain Riemann sums which approximate the iterated integral expression of the multiple zeta values. In this paper, we describe the…
We prove a duality theorem for certain graded algebras and show by various examples different kinds of failure of tameness of local cohomology.
Combining the derivative operator with a binomial sum from the telescoping method, we establish a family of summation formulas involving generalized harmonic numbers.
A supercongruence is a congruence between rational numbers modulo a power of a prime. In this paper, we give a technique for finding and algorithmically proving supercongruences by expressing terms as infinite series involving certain…
Filliman duality expresses (the characteristic measure of) a convex polytope P containing the origin as an alternating sum of simplices that share supporting hyperplanes with P. The terms in the alternating sum are given by a triangulation…
Direct links between generalized harmonic numbers, linear Euler sums and Tornheim double series are established in a more perspicuous manner than is found in existing literature. We show that every linear Euler sum can be decomposed into a…
A generalized matrix function is a generalization of determinant and permanent function. In this paper, we introduced the formula for the value of a generalized matrix function of a linear sum of permutation matrices. We show that a linear…
We prove that double dualization into the generic algebra for an algebraic theory has some Gelfand- or Stone- duality properties
In this paper we give a systematized treatment to some coincidence situations for multiple summing multilinear mappings which extend, generalize and simplify the methods and results obtained thus far. The application of our general results…
We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the index matrices as stochastic transition matrices of random…
Given r>=n quasi-homogeneous polynomials in n variables, the existence of a certain duality is shown and explicited in terms of generalized Morley forms. This result, that can be seen as a generalization of [3,corollary 3.6.1.4] (where this…