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Fourier coefficients of modular forms of half-integral weight

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References

  1. Abramowitz, M., Stegun, I.: Handbook of mathematical functions. New York: Dover 1965

    Google Scholar 

  2. Goldfeld, D., Hoffstein, J., Patterson, S.J.: On automorphic functions of half-integral weight with applications to elliptic curves. In: Number theory related to Fermat's last theorern, Proc. of a Conf. sponsored by the Vaughn Foundation, ed. N. Koblitz. Progress in Maths. Vol. 26. Boston: Birkhäuser 1982

    Google Scholar 

  3. Gross, D., Zagier, D.: Points de Heegner et dérivées des fonctionsL. Preprint 1983

  4. Kohnen, W.: Beziehungen zwischen Modulformen halbganzen Gewichts und Modulformen ganzen Gewichts. Dissertation. Bonn. Math. Schr.131 (1981)

  5. Kohnen, W.: Newforms of half-integral weight. J. reine angew. Math.333, 32–72 (1982)

    Google Scholar 

  6. Kohnen, W., Zagier, D.: Values ofL-series of modular forms at the center of the critical strip. Invent. Math.64, 175–198 (1981)

    Google Scholar 

  7. Kohnen, W., Zagier, D.: Modular forms with rational periods. In: Modular forms, ed. R.A. Rankin, Ellis Horwood Limited Publishers, Chichester, 1984

    Google Scholar 

  8. Manin, Y.: Periods of parabolic forms andp-adic Hecke series. Math. USSR Sb.,21, 371–393 (1973)

    Google Scholar 

  9. Niwa, S.: Modular forms of half-integral weight and the integral of certain theta-functions. Nagoya Math. J.56, 147–161 (1974)

    Google Scholar 

  10. Niwa, S.: On certain thera functions and modular forms of half-integral weight. Preprint 1983

  11. Rankin, R.A.: The scalar product of modular forms. Proc. Lond. Math. Soc.2, 198–217 (1972)

    Google Scholar 

  12. Sarnak, P.: Class numbers of indefinite binary quadratic forms. J. Number Theory15, 229–247 (1982)

    Article  Google Scholar 

  13. Shimura, G.: The special values of the zeta functions associated with cusp forms. Commun. Pure appl. Math.29, 783–804 (1976)

    Google Scholar 

  14. Shimura, G.: On modular forms of half-integral weight. Ann. Math.97, 440–481 (1973)

    Google Scholar 

  15. Shimura, G.: The critical values of certain zeta functions associated with modular forms of half-integral weight. J. Math. Soc. Japan33, 649–672 (1981)

    Google Scholar 

  16. Shintani, T.: On construction of holomorphic cusp forms of half-integral weight. Nagoya Math. J.58, 83–126 (1975)

    Google Scholar 

  17. Siegel, C.L.: Über die Klassenzahl quadratischer Zahlkörper. Acta Arithm.1, 83–86 (1935)

    Google Scholar 

  18. Waldspurger, J.L.: Correspondances de Shimura et Shintani. J. Math. Pures Appl.59, 1–133 (1980)

    Google Scholar 

  19. Waldspurger, J.L.: Sur les coefficients de Fourier des formes modulaires de poids demi-entier. J. Math. Pures Appl.60, 375–484 (1981)

    Google Scholar 

  20. Zagier, D.: Modular forms associated to real quadratic fields. Invent. Math.30, 1–46 (1975)

    Google Scholar 

  21. Zagier, D.: Modular forms whose Fourier coefficients involve zeta-functions of quadratic fields. In: Modular forms of one variable VI. Lect. Notes Math., vol. 627, pp. 105–169. Berlin, Heidelberg, New York: Springer 1977

    Google Scholar 

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Kohnen, W. Fourier coefficients of modular forms of half-integral weight. Math. Ann. 271, 237–268 (1985). https://doi.org/10.1007/BF01455989

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