Numerical investigation of the properties of remainder in Gauss's circle problem

DOI10.1134/S0965542522120119OpenAlexW4315487898MaRDI QIDQ2679080

D. A. Popov, D. V. Sushko

Publication date: 19 January 2023

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542522120119

zbMATH Keywords

remaindernumerical experimentGauss's circle problemLandau's formularelation between height and width of maximum

Mathematics Subject Classification ID

Fluid mechanics (76-XX) Numerical analysis (65-XX)

Cites Work

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• Sign changes of \(E(T)\), \(\Delta(x)\), and \(P(x)\)
• Moments over short intervals
• Distribution of the error term for the number of lattice points inside a shifted circle
• Bounds and behaviour of the quantities $ P(x)$, $ \Delta(x)$ on short intervals
• A Calculation of the Number of Lattice Points in the Circle and Sphere
• Decoupling for Perturbed Cones and the Mean Square of $|\zeta (\frac 12+it)|$
• The distribution and moments of the error term in the Dirichlet divisor problem
• Circle problem and the spectrum of the Laplace operator on closed 2-manifolds
• The Number of Lattice Points in a k-Dimensional Hypersphere
• Experiments on the Lattice Problem of Gauss

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