# Kloosterman sums in residue classes

Valentin Blomer; Djordje Milićević

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 1, page 51-69
- ISSN: 1435-9855

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topBlomer, 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 -

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