摘要:

A modelMof cardinality λ is said to have the small index property if for everyG⊆ Aut(M) such that [Aut(M) :G] ⩽ λ there is anA⊆Mwith |A|<λ such that AutA(M) ⊆G. We show that ifM*is a saturated model of an unsuperstable theory of cardinality greater thanTh(M), thenM*has the small index property.

ISSN:0024-6115    

DOI:10.1112/plms/s3-69.3.449

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

A multidimensional continued fraction expansion is given which finds provably good Diophantine approximations for all θ∈Rd. For anyQ>1 it finds some approximation (p,q) ∈ Zd+1with 1 ⩽q⩽Qsatisfying ‖qθ−p‖ ⩽ √d+ 1Q−1/d. This expansion consists of a sequence of reduced lattice bases for a parametrized series of lattice bases Bt(θ) (of different lattices) in GL(d+ 1, R), where the positive real parametertvaries. This parametrized familyBt(θ) forms a geodesic in GL(d+ 1, R), and also projects to a geodesicgθin the Riemannian symmetric spacePd+1of all positive definite symmetric matrices. The multidimensional continued fraction expansion is a ‘cutting sequence’ expansion forgθusing a Minkowski fundamental domain of GL(d+ 1, Z)\Pd+1. This method generalizes to give continued fraction expansions finding good Diophantine approximations to an arbitrary set of linear forms.

ISSN:0024-6115    

DOI:10.1112/plms/s3-69.3.464

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-69.3.489

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-69.3.515

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-69.3.541

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-69.3.576

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/plms/s3-69.3.605

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

A recent joint paper with M. N. Hunter contains convergence theory for some expansions of functions in bilateral series of Legendre functions. This paper contains convergence results for such series when the function expanded has a simple discontinuity at the point of expansion, a situation not previously covered. The method used is almost entirely different from that of the earlier paper; it proceeds via Abel summability and Littlewood's Tauberian Theorem.

ISSN:0024-6115    

DOI:10.1112/plms/s3-69.3.629

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6115    

DOI:10.1112/j.1460-244X.1994.tb00510.x

出版商:Oxford University Press    

年代:1994

数据来源: WILEY