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Analogue of Stickelberger's theorem for real abelian fields
mathematics, Thaine's theorem is an analogue of Stickelberger's theorem for real abelian fields, introduced by Francisco Thaine (1988). Thaine's method has
Thaine's_theorem
Gives information about the Galois module structure of class groups of cyclotomic fields
}}\right)} is a principal ideal. Gross–Koblitz formula Herbrand–Ribet theorem Thaine's theorem Jacobi sum Gauss sum Washington 1997, Notes to chapter 6 Washington
Stickelberger's_theorem
Theorem about consecutive perfect powers
conjecture Mordell curve Ramanujan–Nagell equation Størmer's theorem Tijdeman's theorem Thaine's theorem Weisstein, Eric W., Catalan's conjecture, MathWorld Mihăilescu
Catalan's_conjecture
Theorem in algebraic number theory relating p-adic L-functions and ideal class groups
to Herbrand's theorem (the Herbrand–Ribet theorem). Karl Rubin found a more elementary proof of the Mazur–Wiles theorem by using Thaine's method and Kolyvagin's
Main conjecture of Iwasawa theory
Main_conjecture_of_Iwasawa_theory
Mathematical concept
groups, thus giving bounds on their orders, which in turn has led to deep theorems such as the finiteness of some Tate-Shafarevich groups. This led to Karl
Euler_system
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