# Algebraic number theory: Trending topics

The following are the current most viewed articles on Wikipedia within Wikipedia's Algebraic number theory category. Think of it as a What's Hot list for Algebraic number theory. More info »

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Rank Topic Wikipedia views
1 Integer 7,810 2 Discriminant 1,055 3 Algebraic number 439 4 Quadratic reciprocity 247 5 Algebraic number theory 247 6 Modulus (algebraic number theory) 247 7 Algebraic number field 177 8 Fermat's theorem on sums of two squares 159 9 Ramification 138 10 Algebraic integer 137 11 Herbrand quotient 136 12 Proofs of Fermat's theorem on sums of two squares 129 13 Heegner number 111 14 Unit (ring theory) 93 15 Ideal class group 90 16 Regular prime 89 17 Cyclotomic field 88 18 Hasse principle 86 19 Dedekind domain 84 20 Ring of integers 84 21 Group cohomology 81 22 Formal group 76 23 Galois extension 62 24 Adele ring 54 25 Local field 50 26 Class number problem 49 27 Adelic algebraic group 49 28 Galois module 46 29 Quadratic integer 46 30 Artin's conjecture on primitive roots 45 31 Quadratic field 44 32 Kummer theory 44 33 Discriminant of an algebraic number field 40 34 Dirichlet's unit theorem 38 35 Chebotarev's density theorem 37 36 Galois cohomology 34 37 Cubic reciprocity 33 38 Abelian extension 32 39 Fractional ideal 32 40 Newton polygon 32 41 Landau prime ideal theorem 32 42 Class number formula 30 43 Global field 28 44 Hilbert's twelfth problem 28 45 Proofs of quadratic reciprocity 27 46 Arithmetic dynamics 27 47 Brauer group 25 48 Field norm 24 49 Additive polynomial 22 50 Equivariant L-function 22 51 Norm of an ideal 21 52 Quartic reciprocity 21 53 Class formation 20 54 Cyclotomic character 20 55 Totally real number field 19 56 Abstract analytic number theory 19 57 Dedekind zeta function 18 58 Splitting of prime ideals in Galois extensions 18 59 Drinfel'd module 18 60 Euler system 17 61 Reflection theorem 17 62 Fundamental unit (number theory) 17 63 Fundamental discriminant 16 64 P-adic Hodge theory 16 65 List of algebraic number theory topics 15 66 Extension and contraction of ideals 15 67 Heegner point 14 68 Hilbert's Theorem 90 12 69 Hilbert's ninth problem 12 70 S-unit 12 71 Conductor of an abelian variety 12 72 Brumer–Stark conjecture 12 73 Stark–Heegner theorem 11 74 Different ideal 11 75 Grunwald–Wang theorem 11 76 Leopoldt's conjecture 11 77 Local Fields (book) 11 78 Artin conjecture 10 79 Conductor-discriminant formula 10 80 Supersingular prime (for an elliptic curve) 9 81 Brauer–Siegel theorem 9 82 Rigid analytic space 9 83 Cyclotomic unit 9 84 Compatible system of ℓ-adic representations 9 85 Abhyankar's lemma 8 86 Minkowski's bound 8 87 CM-field 8 88 Biquadratic field 7 89 Elliptic unit 7 90 Landau's algorithm 7 91 Arithmetic and geometric Frobenius 6 92 Ankeny–Artin–Chowla congruence less than 5 views
93 Narrow class group less than 5 views
94 Principal ideal theorem less than 5 views
95 Cubic field less than 5 views
96 Serre's conjecture II (algebra) less than 5 views
97 Gras conjecture less than 5 views
98 Algebraic number theory topics less than 5 views
99 Hasse–Arf theorem less than 5 views
100 Stark conjectures less than 5 views
101 Monogenic field less than 5 views
102 Number fields with class number one less than 5 views
103 Local Tate duality less than 5 views
104 Local Euler characteristic formula less than 5 views

# Encyclopedia

Algebraic number theory is both the study of number theory by algebraic methods and the theory of algebraic numbers.

The main article for this category is Algebraic number theory.

## Subcategories

This category has the following 4 subcategories, out of 4 total.

## Pages in category "Algebraic number theory"

The following 101 pages are in this category, out of 101 total. This list may not reflect recent changes (learn more).

### J

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