In mathematics, a congruence subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple...
27 KB (4,782 words) - 20:18, 14 June 2024
Ramanujan's congruences, congruences for the partition function, p(n), first discovered by Ramanujan in 1919 Congruence subgroup, a subgroup defined by...
2 KB (339 words) - 11:09, 14 May 2024
Modular group (section Congruence subgroups)
0, or 1, so these subgroups are torsion-free groups. (There are other torsion-free subgroups.) The principal congruence subgroup of level 2, Γ(2), is...
25 KB (3,317 words) - 11:59, 8 November 2023
Arithmetic group (redirect from Arithmetic subgroup)
integer. These are always finite-index subgroups and the congruence subgroup problem roughly asks whether all subgroups are obtained in this way. The conjecture...
22 KB (3,301 words) - 14:24, 21 May 2024
In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector...
12 KB (1,702 words) - 04:49, 29 June 2024
Maass wave form (section Congruence subgroups)
( N ) {\displaystyle \Gamma (N)} principal congruence subgroup of level N {\displaystyle N} . A subgroup Γ ⊆ S L 2 ( Z ) {\displaystyle \Gamma \subseteq...
37 KB (8,499 words) - 04:15, 20 August 2024
In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation...
19 KB (3,157 words) - 18:43, 9 May 2024
the ring of modular forms M(Γ) is finitely generated when Γ is a congruence subgroup of SL(2, Z). In 2003, Lev Borisov and Paul Gunnells showed that the...
8 KB (1,061 words) - 08:45, 8 May 2021
a quotient of the complex upper half-plane H by the action of a congruence subgroup Γ of the modular group of integral 2×2 matrices SL(2, Z). The term...
15 KB (2,016 words) - 12:06, 8 November 2023
)} ; they belong to a more general class of finite-index subgroups, congruence subgroups. Any order in a quaternion algebra over Q {\displaystyle \mathbb...
24 KB (3,844 words) - 17:56, 29 January 2024