A List of Integral Representations for the Diagonal of Power Series of a Rational Function
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https://elib.sfu-kras.ru/handle/2311/143737Author:
Senashov, Artem V.
Сенашов, Артем В.
Date:
2021-10Journal Name:
Журнал Сибирского федерального университета. Математика и физика, 2021. Journal of Siberian Federal University. Mathematics & Physics, 2021, 14 (5)Abstract:
In this paper we present integral representations for the diagonals of power series. Such
representations are obtained by lowering the multiplicity of integration for the previously known integral
representation. The procedure for reducing the order of integration is carried out in the framework
of the Leray theory of multidimensional residues. The concept of the amoeba of a complex analytic
hypersurface plays a special role in the construction of new integral representations В работе приводятся интегральные представления для диагоналей степенных рядов.
Такие представления получаются понижением кратности интегрирования для известного ранее
интегрального представления. Процедура понижения кратности реализуется в рамках многомерной теории вычетов Лере. Особую роль в конструкции новых интегральных представлений играет
понятие амебы комплексной аналитической гиперповерхности
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