The Circle Problem of Gauss and the Divisor Problem of Dirichlet—Still Unsolved

DOI10.1080/00029890.2018.1401853zbMath1396.11001OpenAlexW2786938536WikidataQ58297059 ScholiaQ58297059MaRDI QIDQ4576993

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Publication date: 11 July 2018

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00029890.2018.1401853

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Lattice points in specified regions (11P21)

Related Items (9)

Voronoï bound for a generalized divisor function ⋮ Newton polygon and distribution of integer points in sublevel sets ⋮ Gauss circle problem over smooth integers ⋮ Lattice points close to the Heisenberg spheres ⋮ Analogue of a Fock-type integral arising from electromagnetism and its applications in number theory ⋮ Two-parameter identities for divisor sums in algebraic number fields ⋮ The Surprising Accuracy of Benford’s Law in Mathematics ⋮ The final problem: an identity from Ramanujan's lost notebook ⋮ Balanced derivatives, identities, and bounds for trigonometric and Bessel series

Cites Work

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• Recent progress on the Dirichlet divisor problem and the mean square of the Riemann zeta-function
• Weighted divisor sums and Bessel function series. II
• Hecke's functional equation and arithmetical identities
• On the divisor and circle problems
• New omega theorems for two classical lattice point problems
• On the order of zeta(1/2+it) and Delta(R)
• Circle and divisor problems, and double series of Bessel functions
• Weighted divisor sums and Bessel function series
• An Introduction to Ramanujan's "lost" Notebook
• Exponential Sums and Lattice Points II
• Exponential Sums and Lattice Points III
• On higher-power moments of Δ(x) (II)
• Higher-Power Moments of δ(x ), E(t ) and P(x )
• Identities Involving the Coefficients of a Class of Dirichlet Series. I

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