Some applications of smooth bilinear forms with Kloosterman sums

Abstract

We revisit a recent bound of I. Shparlinski and T. P. Zhang on bilinear forms with Kloosterman sums, and prove an extension for correlation sums of Kloosterman sums against Fourier coefficients of modular forms. We use these bounds to improve on earlier results on sums of Kloosterman sums along the primes and on the error term of the fourth moment of Dirichlet $L$-functions.

final version; to appear in the special issue of the Proceedings of the Steklov Institute of Mathematics dedicated to the 125th anniversary of I. M. Vinogradov

References in corpus (2)

• Algebraic trace functions over the primes
• On the exponent of distribution of the ternary divisor function

Cited by in corpus (6)

• The fourth moment of individual Dirichlet L-functions on the critical line
• Bilinear Forms with Kloosterman and Gauss Sums
• Bounds for moments of Dirichlet $L$-functions to a fixed modulus
• Chowla and Sarnak Conjectures for Kloosterman Sums
• Cancellations between Kloosterman sums modulo a prime power with prime arguments
• Bilinear Forms with Exponential Sums with Binomials