Kloosterman sums in residue classes

Valentin Blomer, Djordje Milićević

Type: Article

Publication Date: 2015-02-05

Citations: 22

DOI: https://doi.org/10.4171/jems/498

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.

Locations

arXiv (Cornell University) - View - PDF
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Journal of the European Mathematical Society - View - PDF

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+	On Linnik and Selberg’s Conjecture About Sums of Kloosterman Sums	2009	Peter Sarnak Jacob Tsimerman
+	Topics in Classical Automorphic Forms	1997	Henryk Iwaniec
+	Kloosterman sums and Fourier coefficients of cusp forms	1982	Jean-Marc Deshouillérs Henryk Iwaniec
+	A relation between Dedekind sums and Kloosterman sums	1987	Ilan Vardi
+	The subconvexity problem for Artin L -functions	2002	William Duke John Friedlander H. Iwaniec
+	L-series of Rankin type and their functional equations	1979	Wen-Ch'ing Winnie Li
+	Coefficients of Maass Forms and the Siegel Zero	1994	Jeffrey Hoffstein Paul Lockhart
+ PDF Chat	Primes in arithmetic progressions to large moduli	1986	Enrico Bombieri John Friedlander Henryk Iwaniec
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+ PDF Chat	Bounds for modular L-functions in the level aspect☆	2007	Valentin Blomer Gergely Harcos Philippe Michel