The proof of the central limit theorem for theta sums

DOI10.1215/S0012-7094-81-04848-1zbMath0491.10027MaRDI QIDQ1167201

W. B. Jurkat, J. W. van Horne

Publication date: 1981

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

momentsasymptotic distributioncentral limit theoremlimiting distributiondistribution functionstheta sum

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Estimates on character sums (11L40) Probabilistic theory: distribution modulo (1); metric theory of algorithms (11K99)

Related Items (17)

On the central limit theorem for negatively correlated random variables with negatively correlated squares. ⋮ On the first moment of the Gauss sum ⋮ Strong approximation of lacunary series with random gaps ⋮ Short incomplete Gauss sums and rational points on metaplectic horocycles ⋮ On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s ⋮ THE VALUE DISTRIBUTION OF INCOMPLETE GAUSS SUMS ⋮ Quadratic Weyl sums, automorphic functions and invariance principles ⋮ Trigonometric polynomials with frequencies in the set of squares and divisors in a short interval ⋮ Limit theorems for skew translations ⋮ Limit theorems for theta sums ⋮ Small values of Weyl sums ⋮ Spectral theta series of operators with periodic bicharacteristic flow ⋮ Limiting curlicue measures for theta sums ⋮ The uniform central limit theorem for theta sums ⋮ Trigonometric Polynomials and Lattice Points ⋮ Weyl sums and the Lyapunov exponent for the skew-shift Schrödinger cocycle ⋮ Limiting distributions of theta series on Siegel half-spaces

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