Adelic Approach to Number Fields
A detailed guide to adelic approach to number fields. Covers key methods, mathematical significance, and real-world applications.
Mathematics Category
Algebraic Number Theory
50 articles
≈ 500 min total reading
Analytic Class Number Formula Proof
A detailed guide to analytic class number formula proof. Covers key methods, mathematical significance, and real-world applications.
Arakelov Theory and Arithmetic Surfaces
A detailed guide to arakelov theory and arithmetic surfaces. Covers key methods, mathematical significance, and real-world applications.
Arithmetic of Quadratic Forms
A detailed guide to arithmetic of quadratic forms. Covers key methods, mathematical significance, and real-world applications.
Brauer Group and Class Field Theory
A detailed guide to brauer group and class field theory. Covers key methods, mathematical significance, and real-world applications.
Brauer Group of a Number Field
A detailed guide to brauer group of a number field. Covers key methods, mathematical significance, and real-world applications.
Class Field Theory and Abelian Extensions
A detailed guide to class field theory and abelian extensions. Covers key methods, mathematical significance, and real-world applications.
Class Group and Class Number
A detailed guide to class group and class number. Covers key methods, mathematical significance, and real-world applications.
Composition of Binary Quadratic Forms
A detailed guide to composition of binary quadratic forms. Covers key methods, mathematical significance, and real-world applications.
Counting Ideals by Norm
A detailed guide to counting ideals by norm. Covers key methods, mathematical significance, and real-world applications.
Cubic and Higher Degree Extensions
A detailed guide to cubic and higher degree extensions. Covers key methods, mathematical significance, and real-world applications.
Cyclotomic Fields and Roots of Unity
A detailed guide to cyclotomic fields and roots of unity. Covers key methods, mathematical significance, and real-world applications.
Different and Discriminant Computation
A detailed guide to different and discriminant computation. Covers key methods, mathematical significance, and real-world applications.
Dirichlet Unit Theorem for Units
A detailed guide to dirichlet unit theorem for units. Covers key methods, mathematical significance, and real-world applications.
Discriminant and Different of Extensions
A detailed guide to discriminant and different of extensions. Covers key methods, mathematical significance, and real-world applications.
Eichler Shimura Theory and L Functions
A detailed guide to eichler shimura theory and l functions. Covers key methods, mathematical significance, and real-world applications.
Elliptic Curves and Number Fields
A detailed guide to elliptic curves and number fields. Covers key methods, mathematical significance, and real-world applications.
Fermat Last Theorem Historical Overview
A detailed guide to fermat last theorem historical overview. Covers key methods, mathematical significance, and real-world applications.
Galois Theory of Number Fields
A detailed guide to galois theory of number fields. Covers key methods, mathematical significance, and real-world applications.
Height Functions on Number Fields
A detailed guide to height functions on number fields. Covers key methods, mathematical significance, and real-world applications.
Hensel Lemma and Local Methods
A detailed guide to hensel lemma and local methods. Covers key methods, mathematical significance, and real-world applications.
Hermite Lindemann Theorem on Transcendentals
A detailed guide to hermite lindemann theorem on transcendentals. Covers key methods, mathematical significance, and real-world applications.
Hilbert Class Field and Class Groups
A detailed guide to hilbert class field and class groups. Covers key methods, mathematical significance, and real-world applications.
Hilbert Symbol and Local Global
A detailed guide to hilbert symbol and local global. Covers key methods, mathematical significance, and real-world applications.
Ideal Theory in Dedekind Domains
A detailed guide to ideal theory in dedekind domains. Covers key methods, mathematical significance, and real-world applications.
Index Form Equation in Extensions
A detailed guide to index form equation in extensions. Covers key methods, mathematical significance, and real-world applications.
Iwasawa Theory and Zeta Extensions
A detailed guide to iwasawa theory and zeta extensions. Covers key methods, mathematical significance, and real-world applications.
Kummer Theory and Power Residues
A detailed guide to kummer theory and power residues. Covers key methods, mathematical significance, and real-world applications.
L Functions and Dirichlet Characters
A detailed guide to l functions and dirichlet characters. Covers key methods, mathematical significance, and real-world applications.
Lattice Methods in Algebraic Number
A detailed guide to lattice methods in algebraic number. Covers key methods, mathematical significance, and real-world applications.
Minkowski Bound and Ideal Class
A detailed guide to minkowski bound and ideal class. Covers key methods, mathematical significance, and real-world applications.
Mordell Weil Theorem for Elliptic Curves
A detailed guide to mordell weil theorem for elliptic curves. Covers key methods, mathematical significance, and real-world applications.
Neukirch Uchida Theorem on Absolute Galois
A detailed guide to neukirch uchida theorem on absolute galois. Covers key methods, mathematical significance, and real-world applications.
Number Fields and Algebraic Integers
A detailed guide to number fields and algebraic integers. Covers key methods, mathematical significance, and real-world applications.
P Adic Zeta Functions and Iwasawa
A detailed guide to p adic zeta functions and iwasawa. Covers key methods, mathematical significance, and real-world applications.
Primates of Quadratic Number Fields
A detailed guide to primates of quadratic number fields. Covers key methods, mathematical significance, and real-world applications.
Primes in Arithmetic Progressions Ideals
A detailed guide to primes in arithmetic progressions ideals. Covers key methods, mathematical significance, and real-world applications.
Quadratic Fields and Binary Forms
A detailed guide to quadratic fields and binary forms. Covers key methods, mathematical significance, and real-world applications.
Ray Class Groups and Conductor
A detailed guide to ray class groups and conductor. Covers key methods, mathematical significance, and real-world applications.
Regulator and Dirichlet Units Computation
A detailed guide to regulator and dirichlet units computation. Covers key methods, mathematical significance, and real-world applications.
Relative Extension and Relative Class
A detailed guide to relative extension and relative class. Covers key methods, mathematical significance, and real-world applications.
Representation of Primes by Forms
A detailed guide to representation of primes by forms. Covers key methods, mathematical significance, and real-world applications.
Sato Tate Conjecture and Motives
A detailed guide to sato tate conjecture and motives. Covers key methods, mathematical significance, and real-world applications.
Selmer Groups and Galois Cohomology
A detailed guide to selmer groups and galois cohomology. Covers key methods, mathematical significance, and real-world applications.
Shimura Taniyama Conjecture Overview
A detailed guide to shimura taniyama conjecture overview. Covers key methods, mathematical significance, and real-world applications.
Splitting of Primes in Number Fields
A detailed guide to splitting of primes in number fields. Covers key methods, mathematical significance, and real-world applications.
Stark Heegner Theorem for Class One
A detailed guide to stark heegner theorem for class one. Covers key methods, mathematical significance, and real-world applications.
Stark Units and Brumer Stark Conjecture
A detailed guide to stark units and brumer stark conjecture. Covers key methods, mathematical significance, and real-world applications.
Tsen Theorem and Brauer Groups
A detailed guide to tsen theorem and brauer groups. Covers key methods, mathematical significance, and real-world applications.
Zeta Functions of Number Fields
A detailed guide to zeta functions of number fields. Covers key methods, mathematical significance, and real-world applications.