On the pseudorandomness of the signs of Kloosterman sums

DOI10.1017/S1446788700014543zbMath1063.11023OpenAlexW2147475920MaRDI QIDQ4658699

Joël Rivat, Étienne Fouvry, András Sárközy, Philippe Michel

Publication date: 18 March 2005

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446788700014543

zbMATH Keywords

binary sequencesKloosterman sumspseudorandomnesscorrelation measurewell-distribution measure

Mathematics Subject Classification ID

Gauss and Kloosterman sums; generalizations (11L05) Irregularities of distribution, discrepancy (11K38) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items (19)

GOWERS UNIFORMITY NORM AND PSEUDORANDOM MEASURES OF THE PSEUDORANDOM BINARY SEQUENCES ⋮ Gaussian distributions of Kloosterman sums: vertical and horizontal ⋮ On the correlation measures of subsets ⋮ A study in sums of products ⋮ Chowla and Sarnak conjectures for Kloosterman sums ⋮ Bilinear forms with trace functions over arbitrary sets and applications to Sato-Tate ⋮ On pseudorandom properties of some Dirichlet characters ⋮ CANCELLATIONS BETWEEN KLOOSTERMAN SUMS MODULO A PRIME POWER WITH PRIME ARGUMENTS ⋮ Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions ⋮ On the distribution of Kloosterman sums ⋮ On a problem of D. H. Lehmer ⋮ On a problem of D.H. Lehmer and pseudorandom binary sequences ⋮ A large family of pseudorandom binary lattices ⋮ Distribution of modular inverses and multiples of small integers and the Sato-Tate conjecture on average ⋮ Sums of algebraic trace functions twisted by arithmetic functions ⋮ Cancellations amongst Kloosterman sums ⋮ An inverse theorem for Gowers norms of trace functions over F_p ⋮ New pseudorandom sequences constructed by quadratic residues and Lehmer numbers ⋮ The second moment of twisted modular \(L\)-functions

Cites Work

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• Bilinear forms with Kloosterman fractions
• On the Sato-Tate conjecture for Kloosterman sums
• On the Sato-Tate conjecture for Kloosterman sums. II.
• Lower bounds of exponential sums
• Some extremal functions in Fourier analysis
• Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116)
• On finite pseudorandom binary sequences VII: The measures of pseudorandomness

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