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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:application
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gptkb:geometry_of_numbers
analytic number theory
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gptkbp:asymptoticFormula
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πr^2 + E(r)
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gptkbp:concerns
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lattice points
integer points in the plane
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gptkbp:conjecturedBound
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E(r) = O(r^{1/2+ε})
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gptkbp:errorTerm
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E(r)
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gptkbp:field
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number theory
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gptkbp:generalizes
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lattice point problems in higher dimensions
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https://www.w3.org/2000/01/rdf-schema#label
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Gauss circle problem
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gptkbp:improvedBound
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E(r) = O(r^{131/208})
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gptkbp:introducedIn
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1837
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gptkbp:knownBound
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E(r) = O(r^{2/3})
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gptkbp:namedAfter
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gptkb:Carl_Friedrich_Gauss
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gptkbp:openProblem
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Best possible bound for E(r)
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gptkbp:relatedTo
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gptkb:Dirichlet_divisor_problem
lattice point enumeration
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gptkbp:studiedBy
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gptkb:Carl_Friedrich_Gauss
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gptkbp:type
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Estimate the number of integer points (x, y) such that x^2 + y^2 ≤ r^2.
How many integer lattice points are inside or on a circle centered at the origin with radius r?
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gptkbp:bfsParent
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gptkb:Dirichlet_divisor_problem
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gptkbp:bfsLayer
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6
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