Remark on Fourier coefficients of modular forms of half integral weight belonging to Kohnen's spaces

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The purpose of this paper is to derive that the square of Fourier coefficients a(n) at a square free positive integer n of modular forms f of half integral weight belonging to Kohnen's spaces of arbitrary odd level and of arbitrary primitive character is essentially equal to the critical value of the zeta function attached to the modular form F of integral weight which is the image of f under the Shimura correspondence. Previously, Kohnen-Zagier had obtained an analogous result in the case of Kohnen's spaces of square free level and of trivial character. Our results give some generalizations of them of Kohnen-Zagier. Our method of the proof is similar to that of Shimura's paper concerning Fourier coefficients of Hilbert modular forms of half integral weight over totally real fields.

収録刊行物

  • Journal of the Mathematical Society of Japan  

    Journal of the Mathematical Society of Japan 51(3), 715-730, 1999-07 

    The Mathematical Society of Japan

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各種コード

  • NII論文ID(NAID)
    10004480745
  • NII書誌ID(NCID)
    AA0070177X
  • 本文言語コード
    ENG
  • 資料種別
    ART
  • ISSN
    00255645
  • NDL 記事登録ID
    4818873
  • NDL 雑誌分類
    ZM31(科学技術--数学)
  • NDL 請求記号
    Z53-A209
  • データ提供元
    CJP書誌  NDL  J-STAGE 
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