A study in sums of products

Abstract

We give a general version of cancellation in exponential sums that arise as sums of products of trace functions satisfying a suitable independence condition related to the Goursat-Kolchin-Ribet criterion, in a form that is easily applicable in analytic number theory.

v2; 41 pages; minor corrections

References in corpus (2)

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

Cited by in corpus (11)

• Kloosterman paths and the shape of exponential sums
• Sums of algebraic trace functions twisted by arithmetic functions
• Nonvanishing of Dirichlet L-functions
• Rankin-Selberg coefficients in large arithmetic progressions
• Roots of $L$-functions of characters over function fields, generic linear independence and biases
• On the distribution of the maximum of cubic exponential sums
• Chowla and Sarnak Conjectures for Kloosterman Sums
• Sum of the $GL(3)$ Fourier coefficients over mixed powers
• A new type of superorthogonality
• Distribution questions for trace functions with values in cyclotomic integers and their reductions
• Shifted convolution sum with weighted average : $GL(3)\times GL(3)$ setup