Geodesic
Schnirelmann's integral and analogy of Cauchy integral theorem for two-dimensional local fields
Čebyševskij sbornik, Tome 21 (2020) no. 3, pp. 39-58

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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: Schnirelmann's integral, analog of Cauchy's integral theorem for two-dimensional local fields. 
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     author = {S. V. Vostokov and T. Yu. Shashkov and S. S. Afanas'eva},
     title = {Schnirelmann's integral and analogy of {Cauchy} integral theorem for two-dimensional local fields},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {39--58},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2020_21_3_a6/}
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S. V. Vostokov; T. Yu. Shashkov; S. S. Afanas'eva. Schnirelmann's integral and analogy of Cauchy integral theorem for two-dimensional local fields. Čebyševskij sbornik, Tome 21 (2020) no. 3, pp. 39-58. http://geodesic.mathdoc.fr/item/CHEB_2020_21_3_a6/