Cite this article as:

Степаненко Д. С. On verification of Brauer's theorem concerning Artin's L-functions of number fields . Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2012, vol. 12, iss. 4, pp. 31-34. DOI: https://doi.org/10.18500/1816-9791-2012-12-4-31-34

Language:

Russian

Heading:

Mathematics

UDC:

501.1

On verification of Brauer's theorem concerning Artin's L-functions of number fields

Authors:

Степаненко Дмитрий Сергеевич, Saratov State University, Russia, Saratov, Astrakhanskaya 83 , stepanenko.dmitry@gmail.com

Abstract:

This paper investigates problem of analytic continuation of Artin's L-functions. One refinement of Brauer's theorem was obtained. It states that in the case of non-main character all possible poles of Artin's L-functions should lay on the critical line.

Key words:

Artin's L-function, Brauer's theorem.

DOI:

https://doi.org/10.18500/1816-9791-2012-12-4-31-34

References

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ческая теория чисел М. : Мир, 1969. С. 310–348.

3. Brauer R. On Artin’s L-series with general group

characters // Ann. of Math. 1947. Vol. 48. P. 502–514.