| Title:
|
On critical values of twisted Artin $L$-functions (English) |
| Author:
|
Wong, Peng-Jie |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
551-555 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give a simple proof that critical values of any Artin $L$-function attached to a representation $\rho $ with character $\chi _{\rho }$ are stable under twisting by a totally even character $\chi $, up to the $\dim \rho $-th power of the Gauss sum related to $\chi $ and an element in the field generated by the values of $\chi _{\rho }$ and $\chi $ over $\mathbb {Q}$. This extends a result of Coates and Lichtenbaum as well as the previous work of Ward. (English) |
| Keyword:
|
Artin $L$-function |
| Keyword:
|
character |
| Keyword:
|
Galois Gauss sum |
| Keyword:
|
special value |
| MSC:
|
11F67 |
| MSC:
|
11F80 |
| MSC:
|
11L05 |
| MSC:
|
11M06 |
| idZBL:
|
Zbl 06738538 |
| idMR:
|
MR3661060 |
| DOI:
|
10.21136/CMJ.2017.0134-16 |
| . |
| Date available:
|
2017-06-01T14:33:09Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146775 |
| . |
| Reference:
|
[1] Coates, J., Lichtenbaum, S.: On $l$-adic zeta functions.Ann. Math. (2) 98 (1973), 498-550. Zbl 0279.12005, MR 0330107, 10.2307/1970916 |
| Reference:
|
[2] Klingen, H.: Über die Werte der Dedekindschen Zetafunktion.Math. Ann. 145 (1962), 265-272 German. Zbl 0101.03002, MR 0133304, 10.1007/BF01451369 |
| Reference:
|
[3] Martinet, J.: Character theory and Artin $L$-functions.Algebraic Number Fields Proc. Symp. London math. Soc., Univ. Durham 1975, Academic Press, London (1977), 1-87. Zbl 0359.12015, MR 0447187 |
| Reference:
|
[4] Neukirch, J.: Algebraic Number Theory.Grundlehren der Mathematischen Wissenschaften 322, Springer, Berlin (1999). Zbl 0956.11021, MR 1697859, 10.1007/978-3-662-03983-0 |
| Reference:
|
[5] Siegel, C. L.: Über die Fourierschen Koeffizienten von Modulformen.Nachr. Akad. Wiss. Göttingen, II. Math.-Phys. Kl. 3 (1970), 15-56 German. Zbl 0225.10031, MR 0285488 |
| Reference:
|
[6] Ward, K.: Values of twisted Artin $L$-functions.Arch. Math. 103 (2014), 285-290. Zbl 1314.11035, MR 3266371, 10.1007/s00013-014-0692-7 |
| . |
