Power-moments of SL 3 ( ℤ ) Kloosterman sums

Goran Djanković

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 3, page 833-845
  • ISSN: 0011-4642

Abstract

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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 ( ℤ ) . We give formulas for the first three moments and a nontrivial bound for the fourth.

How to cite

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Djanković, Goran. "Power-moments of SL$_3(\mathbb {Z})$ Kloosterman sums." Czechoslovak Mathematical Journal 63.3 (2013): 833-845. <http://eudml.org/doc/260679>.

@article{Djanković2013,
abstract = {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.},
author = {Djanković, Goran},
journal = {Czechoslovak Mathematical Journal},
keywords = {power-moment; SL$_3(\mathbb \{Z\})$-Kloosterman sum; power-moment; SL(3,Z)-Kloosterman sum},
language = {eng},
number = {3},
pages = {833-845},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Power-moments of SL$_3(\mathbb \{Z\})$ Kloosterman sums},
url = {http://eudml.org/doc/260679},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Djanković, Goran
TI - Power-moments of SL$_3(\mathbb {Z})$ Kloosterman sums
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 3
SP - 833
EP - 845
AB - 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.
LA - eng
KW - power-moment; SL$_3(\mathbb {Z})$-Kloosterman sum; power-moment; SL(3,Z)-Kloosterman sum
UR - http://eudml.org/doc/260679
ER -

References

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  4. Iwaniec, H., Topics in Classical Automorphic Forms, Graduate Studies in Mathematics 17 AMS, Providence, RI (1997). (1997) Zbl0905.11023MR1474964
  5. Kloosterman, H. D., 10.1007/BF02564120, Acta Math. 49 (1927), 407-464. (1927) MR1555249DOI10.1007/BF02564120
  6. Larsen, M., Appendix to Poincaré series and Kloosterman sums for SL ( 3 , ℤ ) , in The estimation of S L 3 ( ℤ ) Kloosterman sums, Acta Arith. 50 (1988), 86-89. (1988) MR0945275

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