| Title:
|
Power-moments of SL$_3(\mathbb Z)$ Kloosterman sums (English) |
| Author:
|
Djanković, Goran |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
3 |
| Year:
|
2013 |
| Pages:
|
833-845 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Classical Kloosterman sums have a prominent role in the study of automorphic forms on GL$_2$ and further they have numerous applications in analytic number theory. In recent years, various problems in analytic theory of automorphic forms on GL$_3$ have been considered, in which analogous GL$_3$-Kloosterman sums (related to the corresponding Bruhat decomposition) appear. In this note we investigate the first four power-moments of the Kloosterman sums associated with the group SL$_3(\mathbb Z)$. We give formulas for the first three moments and a nontrivial bound for the fourth. (English) |
| Keyword:
|
power-moment |
| Keyword:
|
SL$_3(\mathbb Z)$-Kloosterman sum |
| MSC:
|
11L05 |
| MSC:
|
11T23 |
| idZBL:
|
Zbl 06282114 |
| idMR:
|
MR3125658 |
| DOI:
|
10.1007/s10587-013-0056-7 |
| . |
| Date available:
|
2013-10-07T12:11:41Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143493 |
| . |
| Reference:
|
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| Reference:
|
[2] Bump, D., Friedberg, S., Goldfeld, D.: Poincaré series and Kloosterman sums for SL$(3,\mathbb Z)$.Acta Arith. 50 (1988), 31-89. MR 0945275, 10.4064/aa-50-1-31-89 |
| Reference:
|
[3] Goldfeld, D.: Automorphic Forms and $L$-Functions for the Group GL$(n, \mathbb R)$. With an appendix by Kevin A. Broughan.Cambridge Studies in Advanced Mathematics 99. Cambridge University Press, Cambridge (2006). MR 2254662 |
| Reference:
|
[4] Iwaniec, H.: Topics in Classical Automorphic Forms.Graduate Studies in Mathematics 17 AMS, Providence, RI (1997). Zbl 0905.11023, MR 1474964 |
| Reference:
|
[5] Kloosterman, H. D.: On the representation of numbers in the form $ax^2+by^2 +cz^2+dt^2$.Acta Math. 49 (1927), 407-464. MR 1555249, 10.1007/BF02564120 |
| Reference:
|
[6] Larsen, M.: Appendix to Poincaré series and Kloosterman sums for SL$(3,\mathbb Z)$, in The estimation of $SL_3(\mathbb Z)$ Kloosterman sums.Acta Arith. 50 (1988), 86-89. MR 0945275 |
| . |
