Abstract
In this section, we shall collect together a few group theoretic preliminaries. We begin by reviewing the basic aspects of characters and class functions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Cassels and A. Fröhlich,Algebraic Number Theory, Academic Press, 1967.
H. Davenport, Multiplicative Number Theory, Springer-Verlag, 1980.
R. Foote, Non-monomial characters and Artin’s conjecture, Trans. Amer. Math. Soc., 321 (1990), 261–272.
R. Foote and V. Kumar Murty, Zeros and poles of Artin L-series, Math. Proc. Camb. Phil. Soc., 105 (1989), 5–11.
R. Foote and D. Wales, Zeros of order 2 of Dedekind zeta functions and Artin’s conjecture, J. Algebra, 131 (1990), 226–257.
A. Fröhlich, Galois Module Structure of algebraic integers, Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, 1983.
N. Katz, Galois properties of torsion points of abelian varieties, Invent. Math., 62 (1981), 481–502.
S. Lang, Algebraic Number Theory, Springer-Verlag, 1986.
J. Lagarias and A. M. Odlyzko, Effective versions of the Chebotarev Density Theorem, Algebraic Number Fields,. A. Fröhlich, 409–464, Academic Press, New York, 19
J. Lagarias, H. Montgomery and A. M. Odlyzko, A bound for the least prime ideal in the Chebotarev Density Theorem, Invent. Math., 54 (1979), 271–296.
V. Kumar Murty, Holomorphy of Artin L-functions, in: Proc. Ramanujan Centennial Conference, 55–66, Ramanujan Mathematical Society, Chidambaram, 1987.
V. Kumar Murty, Explicit formulae and the Lang-Trotter conjecture, Rocky Mountain J. Math., 15 (1985), 535-551.
V. Kumar Murty, The least prime which does not split completely, Forum Math., 6 (1994), 555–565.
M. Ram Murty and V. Kumar Murty, Base change and the Birch and Swinnerton-Dyer conjecture, in: A tribute to Emil Grosswald: number theory and analysis, Contemp. Math., 143 (1993), 481–494.
M. Ram Murty V. Kumar Murty and N. Saradha, Modular forms and the Chebotarev Density Theorem, Amer. J. Math., 110 (1988), 253–281.
V. Kumar Murty and J. Scherk, Effective versions of the Chebotarev Density Theorem in the function field case, C.R. Acad. Sci. Paris, 319 (1994), 523–528.
S. Rhoades, A generalization of the Aramata-Brauer theorem, Proc. Amer. Math. Soc., 119 (1993), 357–364.
J.-P. Serre, Linear representations of finite groups, Springer-Verlag, New York, 1977.
J.-P. Serre, Quelques applications du Théorème de Densité de Chebotarev, Publ. Math. IHES, 54 (1981), 123–
H. M. Stark, Some effective cases of the Brauer-Siegel theorem, Invent. Math., 23 (1974), 135–152.
K. Uchida, On Artin L-functions, Tohoku Math. J., 27 (1975), 75–81.
R. W. van der Waall, On a conjecture of Dedekind on zeta functions, Indag. Math., 37 (1975), 83–86.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Basel AG
About this chapter
Cite this chapter
Murty, M.R., Murty, V.K. (1997). Artin L-Functions. In: Non-vanishing of L-Functions and Applications. Progress in Mathematics, vol 157. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8956-8_3
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8956-8_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-5801-3
Online ISBN: 978-3-0348-8956-8
eBook Packages: Springer Book Archive