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gptkbp:instanceOf
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gptkb:mathematical_concept
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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
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gptkbp:errorTerm
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E(r)
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gptkbp:errorTermBound
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E(r) = O(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 counting in higher dimensions
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gptkbp:hasApplication
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gptkb:probability_theory
gptkb:signal_processing
computer graphics
crystallography
physics
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https://www.w3.org/2000/01/rdf-schema#label
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Gauss's circle problem
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gptkbp:improvedBound
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E(r) = O(r^{2/3})
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gptkbp:introducedIn
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1837
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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:geometry_of_numbers
gptkb:Dirichlet_divisor_problem
analytic number theory
lattice point enumeration
Hardy’s circle method
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gptkbp:seeAlso
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gptkb:Pick's_theorem
lattice point enumeration in polygons
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gptkbp:studiedBy
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gptkb:Carl_Friedrich_Gauss
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gptkbp:type
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How many integer lattice points are inside or on a circle centered at the origin with radius r?
Find the number of integer solutions (x, y) to x^2 + y^2 ≤ r^2.
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gptkbp:bfsParent
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gptkb:Pick's_theorem
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gptkbp:bfsLayer
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8
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