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Values ofL-series of modular forms at the center of the critical strip

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References

  1. Cohen, H.: Sums involving the values at negative integers ofL functions of quadratic characters. Math. Ann.217, 277–285 (1975)

    Google Scholar 

  2. Goldfeld, D., Viola, C.: Mean values ofL-functions associated to elliptic, Fermat and other curves at the center of the critical strip. J. of Number Theory11, 309–320 (1979)

    Google Scholar 

  3. Gross, B., Zagier, D.: On the critical values of HeckeL-series. Soc. Math. de France, Mémoire No 2, 49–54 (1980)

    Google Scholar 

  4. Kohnen, W.: Modular forms of half-integral weight onΓ0(4). Math. Ann.248, 249–266 (1980)

    Google Scholar 

  5. Kohnen, W.: Beziehungen zwischen Modulformen halbganzen Gewichts und Modulformen ganzen Gewichts. Bonner Mathematische Schriften 131, Bonn 1981

  6. Manin, Y.: Periods of parabolic forms andp-adic Hecke series. Math. USSR Sbornik21, 371–393 (1973)

    Google Scholar 

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

    Google Scholar 

  8. Niwa, S.: On Shimura's trace formula. Nagoya Math. J.66, 183–202 (1977)

    Google Scholar 

  9. Oda, T.: On modular forms associated with indefinite quadratic forms of signature (2,n−2). Math. Ann.231, 97–144 (1977)

    Google Scholar 

  10. Rallis, S., Schiffmann, G.: Automorphic forms constructed from the Weil representation: holomorphic case. Amer. J. of Math.100, 1049–1122 (1978)

    Google Scholar 

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

    Google Scholar 

  12. Razar, M.: Dirichlet series and Eichler cohomology. To appear in Trans. AMS

  13. Shimura, G.: Sur les intégrales attachées aux formes automorphes. J. Math. Soc. Japan11, 291–311 (1959)

    Google Scholar 

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

    Google Scholar 

  15. Shimura, G.: The special values of the zeta functions associated with cusp forms. Comm. pure and appl. math.29, 783–804 (1976)

    Google Scholar 

  16. Shimura, G.: On the periods of modular forms. Math. Ann.229, 211–221 (1977)

    Google Scholar 

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

    Google Scholar 

  18. Vignéras, M.-F.: Séries thêta des formes quadratiques indéfinies. In: Modular Functions of One Variable VI, Springer Lecture Notes 627, pp. 227–239. Berlin-Heidelberg-New York: Springer-Verlag 1977

    Google Scholar 

  19. Vignéras, M.-F.: Valeur au centre de symétrie des fonctionsL associées aux formes modulaires. Séminaire Delange-Pisot-Poitou, 1980

  20. Waldspurger, J.L.: Correspondances de Shimura et Shintani. J. Math. pures et appl.59, 1–133 (1980)

    Google Scholar 

  21. Waldspurger, J.L.: Sur les coefficients de Fourier des formes modulaires de poids demi-entier. To appear in J. Math. pures et appl.

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

    Google Scholar 

  23. Zagier, D.: Modular forms whose Fourier coefficients involve zeta-functions of quadratic fields. In: Modular Forms of One Variable VI, Springer Lecture Notes 627, pp. 105–169. Berlin-Heidelberg-New York: Springer-Verlag 1977

    Google Scholar 

  24. Zagier, D.: Eisenstein series and the Riemann zeta function. To appear in Proceedings of the International Colloquium on Automorphic Forms, Bombay 1979

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Kohnen, W., Zagier, D. Values ofL-series of modular forms at the center of the critical strip. Invent Math 64, 175–198 (1981). https://doi.org/10.1007/BF01389166

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