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Showing 1-4 of 4 problems

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All CategoriesNumber TheoryCombinatoricsGraph TheoryAlgebraAlgebraic GeometryGeometryTopologyAnalysisPartial Differential EquationsSet TheoryComputer ScienceMathematical Physics

Problem Set

All SetsMillennium Prize ProblemsHilbert's 23 ProblemsBen Green's 100 Open ProblemsDARPA's 23 Mathematical ChallengesSmale's ProblemsLandau's Problems

Status

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HIL-012
Open

Hilbert's 12th Problem: Extension of Kronecker-Weber Theorem

Extend the Kronecker-Weber theorem on abelian extensions of the rationals to any base number field....

L5
Number Theory
345
19
HIL-007
Open

Hilbert's 7th Problem: Transcendence of Certain Numbers

If $\alpha$ is algebraic and irrational, and $\beta$ is algebraic and irrational, is $\alpha^\beta$ transcendental?...

L4
Number Theory
321
18
HIL-009
Open

Hilbert's 9th Problem: Reciprocity Laws

Generalize the reciprocity law of number theory to arbitrary number fields....

L5
Number Theory
234
13
HIL-011
Open

Hilbert's 11th Problem: Quadratic Forms over Algebraic Number Fields

Extend the theory of quadratic forms with algebraic numerical coefficients....

L4
Number Theory
198
11

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