Интеграл Шнирельмана и аналог интегральной теоремы Коши для двумерных локальных полей

Standard

Интеграл Шнирельмана и аналог интегральной теоремы Коши для двумерных локальных полей. / Vostokov, S. V.; Shashkov, T. Yu; Afanas’eva, S. S.

In: Chebyshevskii Sbornik, Vol. 21, No. 3, 22.10.2020, p. 39-58.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{d853a56485c84b09b5ace5c2ef37cff7,

title = "Интеграл Шнирельмана и аналог интегральной теоремы Коши для двумерных локальных полей",

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{\textquoteright}s integral and the proof of an analog of Cauchy{\textquoteright}s integral theorem for two-dimensional local fields. As a consequence, links between the Hilbert symbol and Schnirelmann{\textquoteright}s integral are established.",

keywords = "Analog of cauchy{\textquoteright}s integral theorem for two-dimensional local fields, Schnirelmann{\textquoteright}s integral",

author = "Vostokov, {S. V.} and Shashkov, {T. Yu} and Afanas{\textquoteright}eva, {S. S.}",

year = "2020",

month = oct,

day = "22",

doi = "10.22405/2226-8383-2020-21-3-39-58",

language = "русский",

volume = "21",

pages = "39--58",

journal = "Chebyshevskii Sbornik",

issn = "2226-8383",

publisher = "Тульский государственный педагогический университет им. Л. Н. Толстого",

number = "3",

}

RIS

TY - JOUR

T1 - Интеграл Шнирельмана и аналог интегральной теоремы Коши для двумерных локальных полей

AU - Vostokov, S. V.

AU - Shashkov, T. Yu

AU - Afanas’eva, S. S.

PY - 2020/10/22

Y1 - 2020/10/22

N2 - 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.

AB - 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.

KW - Analog of cauchy’s integral theorem for two-dimensional local fields

KW - Schnirelmann’s integral

UR - http://www.scopus.com/inward/record.url?scp=85101782098&partnerID=8YFLogxK

U2 - 10.22405/2226-8383-2020-21-3-39-58

DO - 10.22405/2226-8383-2020-21-3-39-58

M3 - статья

AN - SCOPUS:85101782098

VL - 21

SP - 39

EP - 58

JO - Chebyshevskii Sbornik

JF - Chebyshevskii Sbornik

SN - 2226-8383

IS - 3

ER -

ID: 85026514