摘要:

LetS= (s1, s2,…) be a collection of relatively prime numbers. The asymptotic properties of the process of sieving bySmay be realized in terms of a stationary random process. In the case whenSis the set of squares of the primes, one may make use of this representation to verify a conjecture of R. Hall: in a ‘typical’ interval of lengthk, the numberSkof square‐free numbers has a probability mass function having orderk−¼in the limit ask→ ∞.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-43.1.1

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-43.1.12

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

LetKbe a field of characteristicp>0, and letGbe a finitep‐group. LetUbe the group of normalized units of the modular group algebraKG. In this paper we study the relation between exp (U) and exp (G). The main result shows that, ifp⩾ 7 and exp(G)3>|G|, thenGandUhave the same exponent. We also show that, in general, exp(U) cannot be bounded above by any fixed function of exp(G).The method involves a reduction to problems in Lie nilpotency indices, which are solved via an extensive study of Lie dimension subgroups. Some results for smallerpare also given.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-43.1.23

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-43.1.37

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

In this sequel to [6], the clique and graph of links of a prime, non‐primitive idealPof the enveloping algebraUof a finite‐dimensional complex solvable Lie algebragare studied. The main result shows that the graph of links ofPis a quotient of the graph of a ‘generic’ primitive ideal containingP. (The cliques and link graphs of the primitive ideals ofUwere analysed in [6].)

ISSN:0024-6107    

DOI:10.1112/jlms/s2-43.1.49

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-43.1.61

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-43.1.76

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-43.1.91

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-43.1.96

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

We show that the Hausdorff dimension δ of a non‐hyperbolic Julia setJ(T) without critical points can be expressed by the smallest zero of the pressure functiont↦P(T, −tlog |T′|). This result is similar to the Bowen‐Manning‐McCluskey formula. The Hausdorff dimension is also shown to be the smallest exponenttεR for which at‐conformal measure in the sense of Sullivan exists. We also prove uniqueness properties oft‐conformal measures, and we prove the absolute continuity of the Hausdorff measureHδwith respect to any δ‐conformal measure.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-43.1.107

出版商:Oxford University Press    

年代:2016

数据来源: WILEY