Geodesic
Kloosterman sums in residue classes
Journal of the European Mathematical Society, Tome 17 (2015) no. 1, pp. 51-69 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/jems/498
Classification : 11-XX, 00-XX
Keywords: Kloosterman sums, Kuznetsov formula, arithmetic progressions, Linnik's conjecture 
@article{JEMS_2015_17_1_a1,
     author = {Valentin Blomer and Djordje Mili\'cevi\'c},
     title = {Kloosterman sums in residue classes},
     journal = {Journal of the European Mathematical Society},
     pages = {51--69},
     year = {2015},
     volume = {17},
     number = {1},
     doi = {10.4171/jems/498},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/498/}
}
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Valentin Blomer; Djordje Milićević. Kloosterman sums in residue classes. Journal of the European Mathematical Society, Tome 17 (2015) no. 1, pp. 51-69. doi: 10.4171/jems/498

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