Cite this article as:

Kuznetsov V. N., Krivobok V. V., Stepanenko D. S. To the Problem of the Integrity of the Artin’s L-functions. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2013, vol. 13, iss. 4, pp. 23-27. DOI: https://doi.org/10.18500/1816-9791-2013-13-4-23-27

Language: 
Russian
Heading: 
Mathematics
UDC: 
501.1

To the Problem of the Integrity of the Artin’s L-functions

Authors: 
Kuznetsov Valentin Nikolaevich, Saratov State University, Russia, Saratov, Astrakhanskaya 83 , KuznetsovVN@info.sgu.ru
Krivobok Valery Victorovich , Saratov State University, Russia, Saratov, Astrakhanskaya 83 , KrivobokVV@info.sgu.ru
Stepanenko Dmitrii Sergeevich, Saratov State University 1, Saratov State University, Russia, 410012, Saratov, Astrahanskaya st., 83 , stepanenko.dmitry@gmail.com
Abstract: 
In this paper was described a class of Artin’s L-functions, each of which is meromorphic, their poles lays on the critical line Re s = 1/2 and coincides with zeroes of Dedekind’s Z-functions of some fields.
Key words: 
L-функция Артина, теорема Брауэра.
DOI: 
https://doi.org/10.18500/1816-9791-2013-13-4-23-27
References
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3. Brauer R. On Artin’s L-series with general group  characters. Ann. of Math., 1947, vol. 48, pp. 502–514.
4. Stepanenko D. S. On verification of Brauer’s Theorem concerning Artin’s L-functions of Number Fields. Izv.Sarat. Univ. N. S. Ser. Math. Mech. Inform., 2012,vol. 12, iss. 4, pp. 31–34 (in Russian).
5. Kargapolov M. I., Merzliakov Iu. I. Osnovy teorii grupp [Fundamentals of Group Theory]. Moscow, Nauka, 1972 (in Russian).
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