Kloosterman sums in residue classes

Blomer, Valentin, and Milićević, Djordje. "Kloosterman sums in residue classes." Journal of the European Mathematical Society 017.1 (2015): 51-69. <http://eudml.org/doc/277495>.

@article{Blomer2015,
abstract = {We prove upper bounds for sums of Kloosterman sums against general arithmetic weight functions. In particular, we obtain power cancellation in sums of Kloosterman sums over arithmetic progressions, which is of square-root strength in any fixed primitive congruence class up to bounds towards the Ramanujan conjecture.},
author = {Blomer, Valentin, Milićević, Djordje},
journal = {Journal of the European Mathematical Society},
keywords = {Kloosterman sums; Kuznetsov formula; arithmetic progressions; Linnik's conjecture; Kloosterman sums; Kuznetsov formula; arithmetic progressions; Linnik's conjecture},
language = {eng},
number = {1},
pages = {51-69},
publisher = {European Mathematical Society Publishing House},
title = {Kloosterman sums in residue classes},
url = {http://eudml.org/doc/277495},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Blomer, Valentin
AU - Milićević, Djordje
TI - Kloosterman sums in residue classes
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 1
SP - 51
EP - 69
AB - We prove upper bounds for sums of Kloosterman sums against general arithmetic weight functions. In particular, we obtain power cancellation in sums of Kloosterman sums over arithmetic progressions, which is of square-root strength in any fixed primitive congruence class up to bounds towards the Ramanujan conjecture.
LA - eng
KW - Kloosterman sums; Kuznetsov formula; arithmetic progressions; Linnik's conjecture; Kloosterman sums; Kuznetsov formula; arithmetic progressions; Linnik's conjecture
UR - http://eudml.org/doc/277495
ER -