Analytic subgroup theorem information

the analytic subgroup theorem is a significant result in modern transcendental number theory. It may be seen as a generalisation of Baker's theorem on...

isomorphic to G. Then, by a version of the closed subgroup theorem, G ′ {\displaystyle G'} is a real-analytic manifold and then, through the local isomorphism...

infinite normal discrete subgroup. An algebraic group over the real or complex numbers may have closed subgroups (in the analytic topology) that do not have...

Lie group if one exists. Also, Cartan's theorem says that every closed subgroup of a Lie group is a Lie subgroup, in particular a smooth submanifold. Hilbert's...

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...

name, there is no purely algebraic proof of the theorem, since any proof must use some form of the analytic completeness of the real numbers, which is not...

usually defined as a discrete subgroup with finite covolume. The terminology introduced above is coherent with this, as a theorem due to Borel and Harish-Chandra...

he was elected as a Member of the Academia Europaea. Analytic subgroup theorem Bézout's theorem Zilber–Pink conjecture "Prof. Dr. David Masser". University...

theorem, introduced by A.A. Rojtman (1980), asserts that, for l prime to char(k), the Albanese map induces an isomorphism on the l-torsion subgroups....

Banach–Stone theorem (operator theory) Banach–Tarski theorem (measure theory) Bang's theorem (geometry) Barban–Davenport–Halberstam theorem (analytic number...

we have the following result: Theorem: Every connected compact Lie group is the quotient by a finite central subgroup of a product of a simply connected...

with maximal compact subgroup K, additional characters come from matrix coefficients of the complementary series, obtained by analytic continuation of the...

are proper subgroups of O(n) or SO(n) have special properties. One of the earliest fundamental results on Riemannian holonomy is the theorem of Borel &...

random sequence of numbers with density given by the prime number theorem. Analytic number theory studies number theory through the lens of continuous...

{\displaystyle \mathbb {T} =\{z\in \mathbb {C} :|z|=1\}.} The circle group forms a subgroup of C × {\displaystyle \mathbb {C} ^{\times }} , the multiplicative group...

coordinates. In complex analytic terms, the Poincaré–Koebe uniformization theorem (a generalization of the Riemann mapping theorem) states that every simply...

the Torelli theorem for complex algebraic K3 surfaces by Ilya Piatetski-Shapiro and Igor Shafarevich (1971), extended to complex analytic K3 surfaces...

of graphs via their fundamental groups. A fundamental theorem of this area is that every subgroup of a free group is free. There are several natural questions...