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research article
Bilinear forms with Kloosterman sums and applications
We prove nontrivial bounds for general bilinear forms in hyper-Kloosterman sums when the sizes of both variables may be below the range controlled by Fourier-analytic methods (Polya-Vinogradov range). We then derive applications to the second moment of cusp forms twisted by characters modulo primes, and to the distribution in arithmetic progressions to large moduli of certain Eisenstein-Hecke coefficients on GL(3). Our main tools are new bounds for certain complete sums in three variables over finite fields, proved using methods from algebraic geometry, especially l-adic cohomology and the Riemann Hypothesis.
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Type
research article
Web of Science ID
WOS:000409276100002
Authors
Publication date
2017
Publisher
Published in
Volume
186
Issue
2
Start page
413
End page
500
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
October 9, 2017