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 Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 996–1010 (Mi semr974)

Real, complex and functional analysis

On computability of multiple integrals by means of a sum of local residues

R. V. Ulvert

Siberian Federal University, pr. Svobodny, 79, 660041, Krasnoyarsk, Russia

Abstract: We consider $n$-fold integrals of meromorphic differential $n$-forms on an $n$-dimensional complex manifold and study the problem of computability of such integrals by means of local (Grothendieck) residues of these forms. This problem is relevant in various fields of theoretical physics (in superstring theory for study of periods of Calabi–Yau manifolds, in particle physics for computation of anomalous magnetic moments of muons). The obtained theorems refine earlier results of A.K. Tsikh and A.P. Yuzhakov.

Keywords: local residue, local cycle, separating cycle.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 1.2604.2017/ï÷

DOI: https://doi.org/10.17377/semi.2018.15.084

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Document Type: Article
UDC: 517.5
MSC: 32A27
Received July 21, 2018, published September 11, 2018

Citation: R. V. Ulvert, “On computability of multiple integrals by means of a sum of local residues”, Sib. Èlektron. Mat. Izv., 15 (2018), 996–1010

Citation in format AMSBIB
\Bibitem{Ulv18} \by R.~V.~Ulvert \paper On computability of multiple integrals by means of a sum of local residues \jour Sib. \Elektron. Mat. Izv. \yr 2018 \vol 15 \pages 996--1010 \mathnet{http://mi.mathnet.ru/semr974} \crossref{https://doi.org/10.17377/semi.2018.15.084} `