190,268 research outputs found

    Multiplicity One Theorems, S-Version

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    We proved three theorems of SS-version of the mulyiplicity one

    Grunwald- Wang Theorem, an Effective Version

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    The main purpose of this note is to establish an effective version of the Grunwald--Wang Theorem, which asserts that given a family of local characters χv\chi^{v} of KvK_{v}^{*} of exponent mm where vSv \in S for a finite set SS of primes of KK, there exists a global character χ\chi of the idele class group CKC_{K} of exponent mm (unless some special case occurs, when it is 2m2 m) whose component at vv is χv\chi^{v}. The effectiveness problem for this theorem is to bound the norm N(χ)N (\chi) of the conductor of χ\chi in terms of KK, mm, SS and N(χv)N (\chi^{v}). The Kummer case (when KK contains μm\mu_{m}) is easy since it is almost an application of the Chinese Remainder Theorem. In this note, we solve this problem completely in general case, and give three versions of bound, one is with \GRH, and the other two are unconditional bounds. These effective results have some interesting applications in concrete situations. To give a simple example, if we fix pp and ll, one gets a good least upper bound for NN such that pp is not an ll--th power mod NN. One also gets the least upper bound for NN such that lrϕ(N)l^{r} \mid \phi (N) and pp is not an ll--th power mod NN. Some part of this note is adopted (with some revision) from my unpublished thesis (2001) (\cite{Wang2001})

    Search for Higgs, Leptoquarks, and Exotics at Tevatron

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    This paper reviews some of the most recent results from the CDF and DZERO experiments on the searches for Standard Model and Non-Standard Model Higgs bosons, and other new phenomena at the Tevatron. Both experiments examine data from proton anti-proton collision at sqrt{s} = 1.96 TeV, of integrated luminosity ~200$ pb**-1 (per experiment), to search for Higgs predicted in the Standard Model and beyond Standard Model, supersymmetric particles in the Gauge Mediated Symmetry Breaking scenario, leptoquarks, and excited electrons. No signal was observed, and limits on the signatures and models are derived.Comment: Contribution to the proceedings of the XXXIX Recontres de Moriond on Electroweak Interactions and Unified Theorie