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All Algebraic Number Theory

This group gathers theorems that study number fields, the algebraic integers within them, and the numbers, such as transcendental constants, that fall outside the ordinary rational and algebraic hierarchy. It covers unit groups and rings of integers in number fields, the arithmetic of elliptic curves over number fields, transcendence results such as the Lindemann-Weierstrass and Gelfond-Schneider theorems, and structural results, including the Weil conjectures, that describe how algebraic equations behave when their solutions are counted over finite fields and number fields alike.

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All Algebraic Number Theory

20 entries

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Sources

1. Algebraic Number Theory (Wikipedia)

WikipediaDiophantus section

Quote, Diophantus section

The beginnings of algebraic number theory can be traced to Diophantine equations, named after the 3rd-century Alexandrian mathematician, Diophantus.

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All Algebraic Number Theory

Baker's Theorem

Cohn's Irreducibility Criterion

Dirichlet's Unit Theorem

Faltings's Theorem

Gelfond-Schneider Theorem

Hasse's Theorem on Elliptic Curves

Hilbert's Irreducibility Theorem

Lindemann-Weierstrass Theorem

Mahler's Theorem

Minkowski's Theorem

Modularity Theorem

Mordell-Weil Theorem

Nagell-Lutz Theorem

Niven's Theorem

Ostrowski's Theorem

Ribet's Theorem

Sato-Tate Theorem

Six Exponentials Theorem

Tunnell's Theorem

Weil Conjectures