Schnirelmann’s integral and analogy of Cauchy integral theorem for two-dimensional local fields
https://doi.org/0.22405/2226-8383-2020-21-3-39-58
Abstract
The problem studied in the thesis arose from the need to find connections between algebraic
field theory and theory of functions. The Cauchy integral theorem, which is one of the most basic
and classical results of the complex analysis, has a discrete analog in the case of one-dimensional
local fields. The natural question then arises whether it is possible to generalize the same result
to two-dimensional local fields. The present paper contains the definition of Schnirelmann’s
integral and the proof of an analog of Cauchy’s integral theorem for two-dimensional local
fields. As a consequence, links between the Hilbert symbol and Schnirelmann’s integral are
established
Keywords
Supporting agencies: Исследование выполнено при поддержке Российского научного фонда (проект 16-11-10200)
About the Authors
Sergey Vladimirovich Vostokov
Saint Petersburg State University
Russian Federation
Doctor of Physical and Mathematical Sciences, Professor
Russian Federation
Doctor of Physical and Mathematical Sciences, Professor
Timofei Yurievich Shashkov
Saint Petersburg State University
Russian Federation
Russian Federation
Sofya Sergeevna Afanas’eva
Saint Petersburg State University
Russian Federation
Russian Federation
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Review
For citations:
Vostokov S.V., Shashkov T.Yu., Afanas’eva S.S. Schnirelmann’s integral and analogy of Cauchy integral theorem for two-dimensional local fields. Chebyshevskii Sbornik. 2020;21(3):39-58. (In Russ.) https://doi.org/0.22405/2226-8383-2020-21-3-39-58
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