The uniform central limit theorem for theta sums

DOI10.1215/S0012-7094-83-05030-5zbMath0524.10029MaRDI QIDQ585267

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

Publication date: 1983

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

zbMATH Keywords

Hardy-Littlewood methodestimate of Kloosterman sumsuniform central limit theorem for theta sums

Mathematics Subject Classification ID

Applications of the Hardy-Littlewood method (11P55) Estimates on character sums (11L40) Probabilistic theory: distribution modulo (1); metric theory of algorithms (11K99) Limit theorems in probability theory (60F99)

Related Items (12)

On the central limit theorem for negatively correlated random variables with negatively correlated squares. ⋮ Short incomplete Gauss sums and rational points on metaplectic horocycles ⋮ THE VALUE DISTRIBUTION OF INCOMPLETE GAUSS SUMS ⋮ Limit laws for rational continued fractions and value distribution of quantum modular forms ⋮ Quadratic Weyl sums, automorphic functions and invariance principles ⋮ On the uniform equidistribution of long closed horocycles ⋮ 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 ⋮ Limiting distributions of theta series on Siegel half-spaces

Cites Work

• Unnamed Item
• The proof of the central limit theorem for theta sums
• On the central limit theorem for theta series
• Über die Kloostermanschen Summen \(S(u,v;q)\)
• An Asymptotic Formula in the Theory of Numbers
• Asymptotic expansions of finite theta series
• On Kloosterman's sum
• On Some Exponential Sums

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