摘要:

Givenkcommuting actionso∈Gof a group or semigroup on a compact spaceXwe aim for the conclusion that for any open coverUwe get someV∈Dand manyd∈GwithV∩T1dV∩…∩T1dT2d…TkdV≠∅.. We obtain this result with additional hypotheses. We apply these results to obtain some van der Waerden type theorems in an arbitrary semigroup. Several counterexamples are then presented to show that both our topological and combinatorial results are the best possible.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.3.385

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

This paper concerns certain two‐dimensional abelian varietiesAwhich are Q‐simple factors ofJ0(N) and have extra twist by the character associated to a quadratic number fieldk. Results of Ribet [22] and Momose [21] are used to give a simple necessary and sufficient condition forAto split overk. TheL‐series ofAoverkis the square of the Mellin transform of a cusp form of weight 2 overkwith rational integer coefficients which, ifAdoes not split overk, is thus not theL‐series of any elliptic curve defined over it. This answers negatively a question raised by the author [5] and others [8,15] in relation to a Weil‐Taniyama conjecture for imaginary quadratic number fields.All examples coming fromJ0(N) withN⩽ 300 are given explicitly. The complex multiplication case is also considered in more detail: ifAhas CM by an imaginary quadratic order θ, it is shown that θ must have class number 1 or 2. An explicit construction is given for these (finitely many) cases.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.3.404

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.3.417

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.3.433

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.3.446

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.3.469

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.3.481

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.3.491

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

In this paper we prove Riesz type theorems on uniqueness sets for regular functions in the Dirichlet class and for meromorphic functions in the spherical Dirichlet class.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.3.508

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

Given a compactly supported function φ: Rδ→ C and the spaceSspanned by its integer translates, we study quasiinterpolants which reproduce (entirely or in part) the spaceHof all exponentials inS. We do this by imitating the action on H of the associated semi‐discrete convolution operator φ∗′ by a convolution λ∗,λ A being a compactly supported distribution, and inverting λ∗|Hby another local convolution operator μ∗. This leads to a unified theory for quasiinterpolants on regular grids, showing that each specific construction now in the literature corresponds to a special choice of λ and μ. The natural choice λ = φ is singled out, and the interrelation between φ∗′ and φ∗ is analysed in detail.We use these observations in the conversion of the approximation order at zero of an exponential spaceHinto approximation rates from any space which containsHand is spanned by thehzs‐translates of a single compactly supported function φ. The bounds obtained are attractive in the sense that they rely only onHand the basic quantities diam supp φ andhs¶φ¶∞/φ(0).

ISSN:0024-6107    

DOI:10.1112/jlms/s2-45.3.519

出版商:Oxford University Press    

年代:2016

数据来源: WILEY