Explicit growth and expansion for sl2

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August undefined, 2024

WebJun 15, 2024 · In Section 5 we exhibit explicit algorithms to decide whether G = 〈 A, B 〉 ≤ SL 2 (R) is discrete. The group G is called elementary if the commutators [ g , h ] = g h g − 1 h − 1 of all pairs g , h ∈ G of infinite order have trace 2. WebGROWTH AND GENERATION IN SL2(Z/pZ) 603 If A equals the projection of a fixed set of generators of a free group in SL/2(Z) (take, e.g., A as in (1.2) or (1.3)) it follows by a simple argument that A must grow rapidly at first when multiplied by itself. In such a situation, we obtain a bound of diam(r(SL2(Z/pZ), A)) < logp,

Explicit Growth and Expansion for SL2 - RERO DOC

WebOct 23, 2024 · Explicit Growth and Expansion for SL2 Article Jan 2012 Emmanuel Kowalski View Show abstract Bounds for multiplicities of automorphic representations … WebDownload Citation Explicit Growth and Expansion for SL2 We give explicit versions of Helfgott's Growth Theorem for $\SL_2$, as well as of the Bourgain-Gamburd … early childhood professional organizations

arXiv:1201.1139v3 [math.NT] 2 Jul 2012

WebSep 30, 2010 · We prove that Cayley graphs of SL2 (Fp) are expanders with respect to the projection of any fixed elements in SL (2, Z) generating a non-elementary subgroup, and with respect to generators chosen at… Expand 284 PDF View 6 excerpts, references methods and background Finite groups of uniform logarithmic diameter Miklós Abért, L. … WebApplying this method straightforwardly with explicit estimates (as done in [16, Chapter 4]), one obtains explicit expansion bounds (either for the spectral gap of the combinatorial … WebWe give explicit versions of Helfgott's Growth Theorem for SL2, as well as of the Bourgain-Gamburd argument for the expansion of Cayley graphs modulo primes of subgroups of SL2(Z) which are Zariski-dense in SL2 Kowalski, Emmanuel ... Explicit Growth and Expansion for SL2 Kowalski, Emmanuel In: International Mathematics Research … early childhood professional

$Expansion in SL 2 ${(\mathbb{R})}$ and monotone …$

Growth and generation in SL2(Z/pZ) - JSTOR

WebIn the case of SL(2;Z) there is a more elementary computation (see [10, p. 88]) which shows that dimM k(SL(2;Z)) = ( bk=12c if k= 2 mod 12;k 0 bk=12c+ 1 for other k 0: : The space dimM k(0(N)) is the direct sum of dimS k(0(N)) and the space of Eisenstein series. WebJul 1, 2024 · We give explicit versions of Helfgott's Growth Theorem for $\SL_2$, as well as of the Bourgain-Gamburd argument for expansion of Cayley graphs modulo primes of subgroups of $\SL_2(\Zz)$ which are ... css 里边框WebJan 13, 2014 · We give explicit versions of Helfgott's Growth Theorem for $\SL_2$, as well as of the Bourgain-Gamburd argument for expansion of Cayley graphs modulo primes … early childhood professional beliefs

"Webhttp://hdl.handle.net/20.500.11850/60769. dc.identifier.doi. 10.3929/ethz-b-000060769 " - Explicit growth and expansion for sl2

Explicit growth and expansion for sl2

WebFeb 8, 2013 · This work presents an explicit construction of a family of monotone expanders, which are bi-partite expander graphs whose edge-set is defined by (partial) … WebSep 1, 2013 · Note: since we are estimating growth rates and binomial coefficients can be defined for non-integers we are going to ignore the fact that a is not an integer in the next lemma. Lemma 5.6.2. Let a = (1 2 − 5 10) n − 1 then the growth rate of (n − a a + 1) is exponential in n. Proof. Stirlingʼs formula says n! ∼ 2 π n (n e) n. (The ∼ ...

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WebE. Kowalski (2013) “Explicit Growth and Expansion for SL2,” International Mathematics Research Notices, Vol. 2013, No. 24, pp. 5645–5708 Advance Access Publication October 7 WebJan 5, 2012 · Explicit growth and expansion for SL_2 Emmanuel Kowalski We give explicit versions of Helfgott's Growth Theorem for $\SL_2$, as well as of the Bourgain-Gamburd argument for expansion of Cayley graphs modulo primes of subgroups of $\SL_2 (\Zz)$ which are Zariski-dense in $\SL_2$ . Submission history From: Emmanuel …

WebThen I will describe how the adjoint twisted Reidemeister torsion shows up in the asymptotic expansion of the invariants. Especially, we find new explicit formulas for the adjoint twisted Reidemeister torsion of the fundamental shadow link complements and of the 3-manifolds obtained by doing hyperbolic Dehn-filling on those link complements. WebSep 17, 2024 · Every matrix A ∈ SL2(Z[1 / p]) is a product of at most 5 elementary matrices as was proved by Vsemirnov (ref. 1, theorem 1.1). The key difference between Z and Z[1 / p] for this bounded generation question for SL2 is their units: Z …

WebApr 16, 2015 · Expander graphs are an important tool in theoretical computer science, geometric group theory, probability, and number theory. Furthermore, the techniques used to rigorously establish the... WebAbstract. We give explicit versions of Helfgott’s Growth Theorem for SL2, as well as of the Bourgain-Gamburd argument for expansion of Cayley graphs modulo primes of subgroups of SL2(Z) which are Zariski-dense in SL2. Contents 1. Introduction 1 2. Explicit multiplicative combinatorics 4 3. Growth for SL2 5 4. The Bourgain-Gamburd method 19 5.

WebarXiv:1201.1139v1 [math.NT] 5 Jan 2012 EXPLICIT GROWTH AND EXPANSION FOR SL2 EMMANUEL KOWALSKI Abstract. We give explicit versions of Helfgott’s Growth Theorem for SL2, as well

WebWe give explicit versions of Helfgott's Growth Theorem for SL2, as well as of the Bourgain-Gamburd argument for the expansion of Cayley graphs modulo primes of subgroups of … early childhood profile ky statsWebSep 27, 2024 · The proofs proceed from some recent estimates for the asymptotic size of Qm(x). Thereafter, the argument is combinatorial. View Show abstract On the growth rate in SL2(Fp)${\rm SL_2}(\mathbb... early childhood professional definitionWebExplicit growth and expansion for SL_2 Explicit growth and expansion for SL_2. Access Restriction Open. Author: Kowalski, Emmanuel: Source: arXiv.org: Content type: Text: File Format: PDF: Language: English: Learning Resource Type: Article: Explicit growth and expansion for SL_2. Select any item from the right-pane. css 重ねる flex