Kloosterman sums in residue rings

• Autorzy: J. Bourgain , M. Z. Garaev
• Języki publikacji: EN

Abstrakty

EN

We generalize some of our previous results on Kloosterman sums [Izv. Mat., to appear] for prime moduli to general moduli. This requires establishing 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 moduli.

Kategorie tematyczne

• 11L05: Gauss and Kloosterman sums; generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 164
• Numer: 1
• Strony: 43-64

Daty

wydano

2014

Twórcy

autor

J. Bourgain

• Institute for Advanced Study, Princeton, NJ 08540, U.S.A.

autor

M. Z. Garaev

• Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Morelia 58089, Michoacán, México

Identyfikatory

DOI

10.4064/aa164-1-4