Jugendtraum
Kronecker 
proved that all the Galois extensions of the RationalsQ with Abelian Galois groups are Subfields of cyclotomicfields 
, where 
is the group of 
th Roots of Unity. He then sought to find asimilar function whose division values would generate the Abelian extensions of an arbitrary Number Field. Hediscovered that the j-Function works for Imaginary quadratic number fields 
, but thecompletion of this problem, known as Kronecker's Jugendtraum (``dream of youth''), for other fields remains one of the greatunsolved problems in Number Theory.
References
Shimura, G. Introduction to the Arithmetic Theory of Automorphic Functions. Princeton, NJ: Princeton University Press, 1981.
- Homothecy
- Homothetic
- Homothetic Center
- Homothetic Position
- Homothetic Triangles
- Homotopy
- Homotopy Axiom
- Homotopy Group
- Homotopy Theory
- Honeycomb
- Hoof
- Hook
- Hook Length Formula
- Hopf Algebra
- Hopf Bifurcation
- Hopf Circle
- Hopf Link
- Hopf Map
- Hopf's Theorem
- Horizontal
- Horizontal-Vertical Illusion
- Horn Angle
- Horn Cyclide
- Horned Sphere
- Horner's Method