Some applications of smooth bilinear forms with Kloosterman sums

DOI10.1134/S0081543817010023zbMath1376.11063arXiv1604.07664MaRDI QIDQ2362389

Valentin Blomer, Djordje Milićević, Emmanuel Kowalski, Philippe Michel, Étienne Fouvry

Publication date: 7 July 2017

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.07664

zbMATH Keywords

modular form\(L\)-functionKloosterman sumshifted convolution sumincomplete exponential sum.

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Exponential sums (11T23) Gauss and Kloosterman sums; generalizations (11L05) Holomorphic modular forms of integral weight (11F11) Estimates on character sums (11L40) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items

Bilinear sums of Gauss sums ⋮ Congruences with intervals and arbitrary sets ⋮ Trilinear forms with double Kloosterman sums ⋮ On the error term in a mixed moment of L‐functions ⋮ The fourth moment of Dirichlet \(L\)-functions along the critical line ⋮ Limit laws for rational continued fractions and value distribution of quantum modular forms ⋮ The fourth moment of Dirichlet \(L\)-functions at the central value ⋮ Bounds on bilinear forms with Kloosterman sums ⋮ Chowla and Sarnak conjectures for Kloosterman sums ⋮ Bilinear forms with Kloosterman and Gauss sums in function fields ⋮ Bilinear forms with exponential sums with binomials ⋮ CANCELLATIONS BETWEEN KLOOSTERMAN SUMS MODULO A PRIME POWER WITH PRIME ARGUMENTS ⋮ On sums of Kloosterman and Gauss sums ⋮ Double sums of Kloosterman sums in finite fields ⋮ The fourth moment of individual Dirichlet \(L\)-functions on the critical line ⋮ Mollification of the fourth moment of Dirichlet $L$-functions ⋮ Bounds on bilinear sums of Kloosterman sums

Cites Work

• The fourth moment of Dirichlet \(L\)-functions
• Rankin-Selberg \(L\)-functions in the level aspect.
• Algebraic twists of modular forms and Hecke orbits
• Algebraic trace functions over the primes
• Cancellations amongst Kloosterman sums
• On moments of twisted L-functions
• Prime Numbers in Short Intervals and a Generalized Vaughan Identity
• ON THE EXPONENT OF DISTRIBUTION OF THE TERNARY DIVISOR FUNCTION

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