Hyperfunctions, formal groups and generalized Lipschitz summation formulas
type: Item
instance of: scholarly article
title: Hyperfunctions, formal groups and generalized Lipschitz summation formulas
zbMATH Open document ID: 1254.43008
author: Stefano Marmi
author: Piergiulio Tempesta
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2012-05-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/0712.1046
review text: The purpose of the paper is to establish a connection between hyperfunctions and some topics of mathematical physics and analytic number theory. The authors relate hyperfunctions with formal groups and generalizations of the classical Lipschitz formula. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli type polynomials related to the Lazard formal group. They finally study the class of Appell polynomials, that is a more general class of Bernoulli type polynomials, to construct associate families of hyperfunctions.
reviewed by: Dohan Kim
Mathematics Subject Classification ID: 43A35
Mathematics Subject Classification ID: 46F15
Mathematics Subject Classification ID: 43A55
Mathematics Subject Classification ID: 33C65
zbMATH DE Number: 6030566
zbMATH Keywords: hyperfunction
zbMATH Keywords: polylogarithm
zbMATH Keywords: Lazard formal group
zbMATH Keywords: Lipschitz summation formula
MaRDI profile type: Publication
OpenAlex ID: W2143230827
arXiv ID: 0712.1046
cites work: Q3999037
cites work: Classical microlocal analysis in the space of hyperfunctions
cites work: Complex Brjuno functions
cites work: Infinite-dimensional Frobenius manifolds for \(2+1\) integrable systems
cites work: Automorphic forms, hyperfunction cohomology, and period functions.
cites work: Laplace's Integral, the Gamma Function, and beyond
cites work: Lie algebras and Lie groups. 1964 lectures, given at Harvard University.
cites work: Formal groups, Bernoulli-type polynomials and \(L\)-series
cites work: A generalization of the Lipschitz summation formula and some applications
cites work: Q4692951
cites work: Hyperfunctions and theoretical physics. Rencontre de Nice, 21-30 Mai 1973
cites work: Q4001952
cites work: The Dilogarithm Function
cites work: Q4283465
cites work: Q3901604
cites work: FORMAL GROUPS AND THEIR ROLE IN THE APPARATUS OF ALGEBRAIC TOPOLOGY
cites work: The Universal Von Staudt Theorems
cites work: On Appell sequences of polynomials of Bernoulli and Euler type
cites work: Q3939864
cites work: On the Kummer Congruences and the Stable Homotopy of BU
cites work: Q3475991
cites work: Universal higher order Bernoulli numbers and Kummer and related congruences
cites work: Bounds of divided universal Bernoulli numbers and universal Kummer congruences
DOI: 10.1016/J.NA.2011.09.013
description: scientific article; zbMATH DE number 6030566