ON THE FOURIER COEFFICIENTS OF MODULAR FORMS OF HALF INTEGRAL WEIGHT BELONGING TO KOHNEN'S SPACES AND THE CRITICAL VALUES OF ZETA FUNCTIONS

この論文にアクセスする

この論文をさがす

著者

抄録

The purpose of this paper is to derive a generalization of Kohnen-Zagier's results concerning Fourier coefficients of modular forms of half integral weight belonging to Kohnen's spaces, and to refine our previous results concerning Fourier coefficients of modular forms of half integral weight belonging to Kohnen's spaces. Employing kernel functions, we construct a correspondence $\varPsi$ from modular forms of half integral weight $k+1/2$ belonging to Kohnen's spaces to modular forms of weight $2k$. We explicitly determine the Fourier coefficients of $\varPsi(f)$ in terms of those of $f$. Moreover, under certain assumptions about $f$ concerning the multiplicity one theorem with respect to Hecke operators, we establish an explicit connection between the square of Fourier coefficients of $f$ and the critical value of the zeta function associated with the image $\varPsi(f)$ of $f$ twisted with quadratic characters, which gives a further refinement of our results concerning Fourier coefficients of modular forms of half integral weight belonging to Kohnen's spaces.

収録刊行物

  • Tohoku Mathematical Journal, Second Series

    Tohoku Mathematical Journal, Second Series 56(1), 125-145, 2004

    東北大学

各種コード

  • NII論文ID(NAID)
    110000027035
  • NII書誌ID(NCID)
    AA00863953
  • 本文言語コード
    ENG
  • ISSN
    0040-8735
  • データ提供元
    NII-ELS  J-STAGE 
ページトップへ