Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter March 10, 2020

Artin L-functions of almost monomial Galois groups

Mircea Cimpoeaş and Florin Nicolae
From the journal Forum Mathematicum

Abstract

If K/ is a finite Galois extension with an almost monomial Galois group and if s0{1} is not a common zero for any two Artin L-functions associated to distinct complex irreducible characters of the Galois group, then all Artin L-functions of K/ are holomorphic at s0. We present examples and basic properties of almost monomial groups.

MSC 2010: 11R42; 20C15

Communicated by Freydoon Shahidi


References

[1] E. Artin, Zur Theorie der L-Reihen mit allgemeinen Gruppencharakteren, Abh. Math. Semin. Univ. Hambg. 8 (1931), 292–306. 10.1007/BF02941010Search in Google Scholar

[2] G. James and A. Kerber, The Representation Theory of the Symmetric Group, Addison-Wesley, Boston, 1991. Search in Google Scholar

[3] F. Nicolae, On holomorphic Artin L-functions, Monatsh. Math. 186 (2018), no. 4, 679–683. 10.1007/s00605-017-1120-4Search in Google Scholar

[4] The GAP Group, GAP – Groups, Algorithms, and Programming, Version 4.10.2; 2019, https://www.gap-system.org. 10.1093/oso/9780190867522.003.0002Search in Google Scholar

Received: 2019-10-21
Revised: 2020-02-11
Published Online: 2020-03-10
Published in Print: 2020-07-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Scroll Up Arrow