Chowla and Sarnak Conjectures for Kloosterman Sums

Abstract

We formulate several analogues of the Chowla and Sarnak conjectures, which are widely known in the setting of the Möbius function, in the setting of Kloosterman sums. We then show that for Kloosterman sums, in some cases, these conjectures can be established unconditionally.

References in corpus (19)

• An averaged form of Chowla's conjecture
• Algebraic trace functions over the primes
• The Möbius function and distal flows
• On moments of twisted $L$-functions
• Automatic sequences fulfill the Sarnak conjecture
• The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures
• Sums of Kloosterman sums in arithmetic progressions, and the error term in the dispersion method
• A study in sums of products
• The Shifted Convolution of Divisor Functions
• The structure of correlations of multiplicative functions at almost all scales, with applications to the Chowla and Elliott conjectures
• Some applications of smooth bilinear forms with Kloosterman sums
• Higher uniformity of bounded multiplicative functions in short intervals on average
• Kloosterman sums and Fourier coefficients of Eisenstein series
• Mobius disjointness conjecture for local dendrite maps
• Kloosterman sums in residue classes
• Sums of algebraic trace functions twisted by arithmetic functions
• Sign changes of Kloosterman sums and exceptional characters
• On a Twisted Version of Linnik and Selberg's Conjecture on Sums of Kloosterman Sums
• Stratification and averaging for exponential sums: bilinear forms with generalized Kloosterman sums

Cited by in corpus (1)

• Kloosterman sums do not correlate with periodic functions