...ion by A.O. Gel'fond of Hilbert's seventh problem and from subsequent work of A. Baker. The Gel'fond–Baker method also incorporates ideas due to C.L. S
1) integer points on curves of genus $ 0 $
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The Schur index of a central simple algebra $ A $
cf. [[Central simple algebra|Central simple algebra]]) is the degree of the division algebra $ D $
3 KB (533 words) - 08:12, 6 June 2020
The ''Hasse invariant'' is an arithmetic invariant of various objects.
The Hasse invariant $h(A)$ of a central simple algebra $A$ over a local
8 KB (1,182 words) - 22:00, 5 March 2012
...rphic images of Chernikov groups are also Chernikov; further, an extension of a Chernikov group by a Chernikov group is again Chernikov.
...are two-generator infinite simple groups in which every proper subgroup is of prime order $p$.
4 KB (589 words) - 18:19, 15 January 2017
Out of 131 formulas, 131 were replaced by TEX code.-->
...ts , n$, $i \neq j$, $a \in F$, let $x _ { i j } ( a )$ denote the element of $G$ which differs from the identity matrix only in the $( i , j )$-entry, w
8 KB (1,339 words) - 16:56, 1 July 2020
...group of finite index in $\def\O{\mathcal{O}}G_\O$, where $\O$ is the ring of integers in an algebraic number field $k$ (cf.
...ng $c(G) = 1$. In its modern form, the congruence subgroup problem is that of computing the congruence subgroup kernel $c(G)$.
4 KB (613 words) - 21:48, 5 March 2012
Out of 64 formulas, 64 were replaced by TEX code.-->
...solution over $\mathbf{F} [ T ]$, with $\mathbf{F}$ the algebraic closure of $\mathbf{F}$.
4 KB (702 words) - 16:45, 1 July 2020
be the ring of integers of an algebraic number [[Field|field]] $ F $(
which is also called the tame kernel of $ F $,
5 KB (731 words) - 08:21, 26 March 2023
Out of 445 formulas, 443 were replaced by TEX code.-->
...roup this reduction is carried out with respect to the field of definition of the group.
33 KB (5,081 words) - 10:26, 11 November 2023
is an integer, the power function is a particular case of a [[Rational function|rational function]]. When $ x $
is a [[Power|power]], and the properties of $ y = x ^ {a} $
6 KB (860 words) - 17:32, 6 January 2024
By a [[modular form]] of weight $k$ one understands a function $f$ on the upper half-plane satisfyin
is an element of some congruence subgroup of $\text{SL}(2,\mathbf{Z})$ (cf. also [[Modular function]]).
7 KB (1,047 words) - 17:38, 17 March 2024
of order $ n $,
is the transposed matrix of $ H $
5 KB (775 words) - 11:01, 17 March 2023
of rational numbers by adjoining a primitive $ n $-th root of unity $ \zeta _ {n} $,
is the field of rational $ p $-adic numbers. Since $ K _ {n} = K _ {2n} $
12 KB (1,769 words) - 11:19, 26 March 2023
The notion of ''discriminant'' can have different meanings, depending on the context.
====Discriminant of a [[polynomial]]====
16 KB (2,947 words) - 08:53, 9 December 2016
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...s of characteristic zero is used for various purposes, mainly in the proof of the [[Lefschetz formula|Lefschetz formula]] and its application to zeta-fun
6 KB (932 words) - 11:49, 8 April 2023
of vectors in a vector space $ V $
of the space $ V ^{*} $
22 KB (3,351 words) - 19:14, 21 December 2019
on the set of integers that satisfies the following conditions:
...hmetic progressions. He developed the fundamental principles of the theory of Dirichlet characters [[#References|[2]]]–[[#References|[8]]], starting fr
10 KB (1,462 words) - 11:49, 26 March 2023
is [[#References|[a5]]] the unique [[Galois extension|Galois extension]] of $ \mathbf Z/ {p ^ {m} } \mathbf Z $
of degree $ d $.
7 KB (1,070 words) - 19:40, 5 June 2020
...f mathematics on the other, have determined the development of the concept of a number.
...provided by linguistics and ethnography. Primitive man clearly had no need of counting skills to determine whether or not a given collection was complete
23 KB (3,482 words) - 08:03, 6 June 2020
Out of 186 formulas, 168 were replaced by TEX code.-->
...ups|Quantum groups]]) and a [[Super-group|super-group]], in which the role of Bose–Fermi statistics is now played by more general braid statistics. The
21 KB (3,130 words) - 17:42, 1 July 2020