2013/09/04 by Jean Bourgain, Bourgain, J., M. Z. Garaev +1
Computer Science · Mathematics · #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1309.1124
openalex publication_date 2013/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present paper, we generalize some of the results on Kloosterman sums proven in \citeBG for prime moduli to general moduli. This requires to establish the corresponding additive properties of the reciprocal set I-1=\x-1: x∈ I\, where I is an interval in the ring of residue classes modulo a large positive integer. We apply our bounds on multilinear exponential sums to the Brun-Titchmarsh theorem and the estimate of very short Kloosterman sums, hence generalizing our earlier work to the setting of general modulus.