90 research outputs found

    Poles of the Standard -function of and the Rallis–Schiffmann Lift

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    AbstractWe characterize the cuspidal representations ofG2G_{2}whose standardL{\mathcal{L}}-function admits a pole ats=2s=2as the image of the Rallis–Schiffmann lift for the commuting pair (SL~2\widetilde{\text{SL}}_{2},G2G_{2}) inSp~14\widetilde{\text{Sp}}_{14}. The image consists of non-tempered representations. The main tool is the recent construction, by the second author, of a family of Rankin–Selberg integrals representing the standardL{\mathcal{L}}-function.</jats:p

    Test Vectors for Archimedean Period Integrals

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    We study period integrals involving Whittaker functions associated to generic irreducible Casselman-Wallach representations of GLn(F)\mathrm{GL}_n(F), where FF is an archimedean local field. Via the archimedean theory of newforms for GLn\mathrm{GL}_n developed by the first author, we prove that newforms are weak test vectors for several period integrals, including the GLn×GLn\mathrm{GL}_n \times \mathrm{GL}_n Rankin-Selberg integral, the Flicker integral, and the Bump-Friedberg integral. By taking special values of these period integrals, we deduce that newforms are weak test vectors for Rankin-Selberg periods, Flicker-Rallis periods, and Friedberg-Jacquet periods. These results parallel analogous results in the nonarchimedean setting proven by the second author, which use the nonarchimedean theory of newforms for GLn\mathrm{GL}_n developed by Jacquet, Piatetski-Shapiro, and Shalika. By combining these archimedean and nonarchimedean results, we prove the existence of weak test vectors for certain global period integrals of automorphic forms.Comment: 42 page

    Test vectors for archimedean period integrals

    No full text
    We study period integrals involving Whittaker functions associated to generic irreducible Casselman-Wallach representations of GLn(F), where F is an archimedean local field. Via the archimedean theory of newforms for GLn developed by the first author, we prove that newforms are weak test vectors for several period integrals, including the GLn × GLn Rankin-Selberg integral, the Flicker integral, and the Bump-Friedberg integral. By taking special values of these period integrals, we deduce that newforms are weak test vectors for Rankin-Selberg periods, Flicker-Rallis periods, and Friedberg-Jacquet periods. These results parallel analogous results in the nonarchimedean setting proved by the second author, which use the nonarchimedean theory of newforms for GLn developed by Jacquet, Piatetski-Shapiro, and Shalika. By combining these archimedean and nonarchimedean results, we prove the existence of weak test vectors for certain global period integrals of automorphic forms

    Sosiaalisen median strategia kuntoon

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    Opinnäytetyössä käydään läpi yrityksen sosiaalisen median strategiaa. Tarkoituksena oli luoda Rallis Furille sosiaalinen media ja hyödyntää sosiaalista mediaa osana liiketoimintaa. Opinnäytetyön tekijä oli mukana toteuttamassa yritykselle sosiaalisen median kanavia, jotka ovat jo yrityksen käytössä. Opinnäytetyö on toiminnallinen, joka muodostuu teoriasta ja konkreettisesta sosiaalisen median markkinointisuunnitelmasta. Sosiaalisen median pääkanavana tulee toimimaan Facebook, Instagram ja kotisivut. Toimeksiantajalta ei löytynyt kyseisiä markkinointiviestinnän kanavia, joten opinnäytetyön tekijä tuli suunnittelemaan kaiken alusta lähtien. Tarkoituksena oli tavoittaa uusia asiakkaita ja lisätä yrityksen näkyvyyttä sosiaalisessa mediassa. Opinnäytetyön teoriaosuus pitää sisällään tavotteiden asettamisen, toteutussuunnitelman, kohderyhmän rajaamisen, aikataulun, budjetin sekä seurannan. Opinnäytetyön tekijä määritteli itse suunnitelmassa käytettävät sosiaalisen median kanavat ja esittelee tulevista sosiaalisen median julkaisuista esimerkkejä. Teorian lähteinä on hyödynnetty alan kirjallisuutta sekä sähköisiä artikkeleita. Sosiaalisen median avulla on mahdollista saada lisää potentiaalisia asiakkaita, jonka takia tämä tekee sosiaalisesta mediasta hyödyllisen markkinointikanavan yritykselle. Samalla sosiaalinen media on yritykselle hyvä väylä saada enemmän näkyvyyttä ja uusia kiinnostuneita asiakkaita.Fixing the strategy at social media The thesis deals with the company's social media strategy. The idea was to create social media for Rallis Fur and utilize social media as part of the business. The author of the thesis was involved in implementing a social media channels, witch are already in action. The thesis is functional, consisting of theory and concrete social media marketing plan. The main channel for social media will be Facebook, Instagram and home pages. These marketing communication channels were not found on the client, so the designer of the thesis was planning everything from the beginning. The goal was to reach new customers and increase the company's visibility in social media. The theoretical part of the Thesis considers the content of the goals set, the implementation plan, the target group definition, the schedule, the budget and the follow-up. The author of the thesis defines the channels of social media themselves and presents an example of future social media publications. Theories of literature and electronic articles are used as sources of the theory. Social media enables the opportunity to get more potential customers, which makes social media a useful marketing channel for a company. At the same time social media is a good business for the company to gain more visibility and new enthusiastic customers....
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