Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:bestKnownBound |
Δ(x) = O(x^{131/416})
|
| gptkbp:classicalResult |
Δ(x) = O(x^{1/2})
|
| gptkbp:concerns |
divisor function
|
| gptkbp:d(n) |
number of positive divisors of n
|
| gptkbp:errorTermNotation |
Δ(x)
|
| gptkbp:field |
number theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Dirichlet divisor problem
|
| gptkbp:importantFor |
central in analytic number theory
|
| gptkbp:namedAfter |
gptkb:Peter_Gustav_Lejeune_Dirichlet
|
| gptkbp:openProblem |
find smallest possible exponent in error term
|
| gptkbp:relatedTo |
gptkb:Gauss_circle_problem
gptkb:Riemann_zeta_function Fourier analysis modular forms lattice point problems |
| gptkbp:studiedBy |
gptkb:Peter_Gustav_Lejeune_Dirichlet
|
| gptkbp:sumExpression |
∑_{n ≤ x} d(n)
|
| gptkbp:type |
asymptotic behavior of sum of divisor function
estimate error term in sum of d(n) for n ≤ x |
| gptkbp:bfsParent |
gptkb:Peter_Gustav_Lejeune_Dirichlet
|
| gptkbp:bfsLayer |
5
|