Spherical functions and local densities on hermitian forms

    Research output: Contribution to journalArticle

    27 Citations (Scopus)

    Abstract

    First we give a formula of spherical functions on certain spherical homogeneous spaces. Then, applying it, we complete the theory of the spherical functions on the space X of nondegenerate unramified hermitian forms on a p-adic number field. More precisely, we give an explicit expression for the spherical functions, prove theorems on the spherical Fourier transforms on the space of Schwartz-Bruhat functions on X, and parametrize of all spherical functions on X. Finally, as an application, we give explicit expressions of local densities of representations of hermitian forms.

    Original languageEnglish
    Pages (from-to)553-581
    Number of pages29
    JournalJournal of the Mathematical Society of Japan
    Volume51
    Issue number3
    Publication statusPublished - 1999 Jul

    Fingerprint

    Hermitian form
    Spherical Functions
    P-adic numbers
    P-adic Fields
    Homogeneous Space
    Number field
    Fourier transform
    Theorem

    Keywords

    • Hermitian forms
    • Local densities
    • Spherical functions

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Spherical functions and local densities on hermitian forms. / Hironaka, Yumiko.

    In: Journal of the Mathematical Society of Japan, Vol. 51, No. 3, 07.1999, p. 553-581.

    Research output: Contribution to journalArticle

    @article{415d1f3b071c4e2497b1d02cf4c361d7,
    title = "Spherical functions and local densities on hermitian forms",
    abstract = "First we give a formula of spherical functions on certain spherical homogeneous spaces. Then, applying it, we complete the theory of the spherical functions on the space X of nondegenerate unramified hermitian forms on a p-adic number field. More precisely, we give an explicit expression for the spherical functions, prove theorems on the spherical Fourier transforms on the space of Schwartz-Bruhat functions on X, and parametrize of all spherical functions on X. Finally, as an application, we give explicit expressions of local densities of representations of hermitian forms.",
    keywords = "Hermitian forms, Local densities, Spherical functions",
    author = "Yumiko Hironaka",
    year = "1999",
    month = "7",
    language = "English",
    volume = "51",
    pages = "553--581",
    journal = "Journal of the Mathematical Society of Japan",
    issn = "0025-5645",
    publisher = "Mathematical Society of Japan - Kobe University",
    number = "3",

    }

    TY - JOUR

    T1 - Spherical functions and local densities on hermitian forms

    AU - Hironaka, Yumiko

    PY - 1999/7

    Y1 - 1999/7

    N2 - First we give a formula of spherical functions on certain spherical homogeneous spaces. Then, applying it, we complete the theory of the spherical functions on the space X of nondegenerate unramified hermitian forms on a p-adic number field. More precisely, we give an explicit expression for the spherical functions, prove theorems on the spherical Fourier transforms on the space of Schwartz-Bruhat functions on X, and parametrize of all spherical functions on X. Finally, as an application, we give explicit expressions of local densities of representations of hermitian forms.

    AB - First we give a formula of spherical functions on certain spherical homogeneous spaces. Then, applying it, we complete the theory of the spherical functions on the space X of nondegenerate unramified hermitian forms on a p-adic number field. More precisely, we give an explicit expression for the spherical functions, prove theorems on the spherical Fourier transforms on the space of Schwartz-Bruhat functions on X, and parametrize of all spherical functions on X. Finally, as an application, we give explicit expressions of local densities of representations of hermitian forms.

    KW - Hermitian forms

    KW - Local densities

    KW - Spherical functions

    UR - http://www.scopus.com/inward/record.url?scp=0012949746&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0012949746&partnerID=8YFLogxK

    M3 - Article

    AN - SCOPUS:0012949746

    VL - 51

    SP - 553

    EP - 581

    JO - Journal of the Mathematical Society of Japan

    JF - Journal of the Mathematical Society of Japan

    SN - 0025-5645

    IS - 3

    ER -