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Mathematische Zeitschrift

, Volume 209, Issue 1, pp 273–287 | Cite as

The Dirichlet series of Koecher and Maaß and modular forms of weight 3/2

  • Siegfried Böcherer
  • Rainer Schulze-Pillot
Article

Keywords

Modular Form Eisenstein Series Dirichlet Series Automorphic Form Quaternion Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [An] Andrianov, A.N.: Euler products corresponding to Siegel modular forms of genus 2. Russ. Math. Surv.29, 45–116 (1974)zbMATHCrossRefMathSciNetGoogle Scholar
  2. [Ar] Arakawa, T.: Dirichlet series corresponding to Siegel's modular forms of degreen with levelN. Tôhoku Math. J., II. Ser.42 261–286 (1990)zbMATHMathSciNetCrossRefGoogle Scholar
  3. [BFH] Bump, D., Friedberg, S., Hoffstein, J.: On Waldspurger's theorem. In: Proceedings of the Montreal Conference on Analytic Number Theory and Modular Forms 1989 (to appear)Google Scholar
  4. [Bö1] Böcherer, S.: Siegel modular forms and theta series. In: Ehrenpreis, L., Gunning, R.C. (eds.) Theta Functions. Proceedings of the AMS Summer Research Institute, Bowdoin College 1987 Providence, RI: Am. Math. Soc. 1989Google Scholar
  5. [Bö2] Böcherer, S.: Bemerkungen über die Dirichletreihen von Koecher und Maaß. Preprint Math. Gottingensis Heft68 (1986)Google Scholar
  6. [BS1] Böcherer, S., Schulze-Pillot, R.: Siegel modular forms and theta series attached to quaternion algebras. Nagoya J. Math.121, 35–96 (1991)zbMATHGoogle Scholar
  7. [BS2] Böcherer, S., Schulze-Pillot, R.: On a theorem of Waldspurger and on Eisenstein series of Klingen type. Math. Ann288, 361–388 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  8. [E] Eichler, M.: The basis problem for modular forms and the traces of the Hecke operators. In: Kuyk, W. (ed.) Modular functions of one variable I. (Lect. Notes Math., vol. 320, pp. 76–151). Berlin Heidelberg New York: Springer 1973CrossRefGoogle Scholar
  9. [Ev] Evdokimov, S.A.: Analytic properties of Euler products for congruence subgroups of Sp2 (ℤ). Math. USSR. Sb.38, 335–363 (1981)zbMATHCrossRefGoogle Scholar
  10. [Gr] Gross, B.: Heights and the special values ofL-series. In: Kisilevsky, H., Labute, J. (eds.), Number Theory. Montreal 1985), (CMS Conf. Proc., vol. 7, pp. 115–187). Providence, RI: Am Math. Soc. 1987Google Scholar
  11. [Hi-Sa] Hijikata, H., Saito, H.: On the representability of modular forms by theta series. In: Kusunoki, Y. et al. (eds.), Number Theory, Algebraic Geometry and Commutative Algebra, in honor of Y. Akizuki, pp. 13–21. Tokyo: Kinokuniya 1973Google Scholar
  12. [Hi-Pi-She] Hijikata, H., Pizer, A., Shemanske, T.: The basis problem for modular forms on Γ0(itN). Mem. Am. Math. Soc.418 (1982)Google Scholar
  13. [Koe] Koecher, M.: Über Dirichletreihen mit Funktionalgleichung. J. Reine Angew. Math.102, 1–23 (1953).MathSciNetGoogle Scholar
  14. [Ko1] Kohnen, W.: Newforms of half-integral weight. J. Reine Angew. Math.333, 32–72 (1982)zbMATHMathSciNetGoogle Scholar
  15. [Ko2] Kohnen, W.: Fourier coefficients of modular forms of half-integral weight. Math. Ann.271, 237–268 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  16. [Ma] Maaß, H.: Modulformen zweiten Grades und Dirichletreihen. Math. Ann.122, 90–108 (1951)CrossRefGoogle Scholar
  17. [Pe] Petersson, H.: Über die Berechnung der Skalarprodukte ganzer Modulformen. Comment. Math. Helv.22, 168–191 (1949)zbMATHCrossRefMathSciNetGoogle Scholar
  18. [Po] Ponomarev, P.: Ternary quadratic forms and Shimura's correspondence. Nagoya Math. J.81, 123–151 (1981)zbMATHMathSciNetGoogle Scholar
  19. [Ra] Rankin, R.: The scalar product of modular forms. Proc. Lond. Math. Soc.3, 198–217 (1952)CrossRefMathSciNetGoogle Scholar
  20. [SP] Schulze-Pillot, R.: Ternary quadratic forms and Brandt matrices. Nagoya Math. J.102, 117–126 (1986)zbMATHMathSciNetGoogle Scholar
  21. [Vi] Vigneras, M.-F.: Arithmétique des algèbres de quaternions. (Lect. Notes Math., vol. 800), Berlin Heidelberg New York: Springer 1980zbMATHGoogle Scholar
  22. [Wa1] Waldspurger, J.L.: Engendrement par des séries thêta de certains espaces de formes modularies. Invent. Math.50, 135–168 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  23. [Wa2] Waldspurger, J.L.: Sur les coefficients de Fourier des formes modulaires de poids demi-entier. J. Math. Pures Appl.60, 375–384 (1981)zbMATHMathSciNetGoogle Scholar
  24. [Wa3] Waldspurger, J.L.: Correspondance de, Shimura et quaternions. Forum. Math.3, 219–307 (1991)zbMATHMathSciNetCrossRefGoogle Scholar
  25. [Y1] Yoshida, H.: Siegel's modular forms and the arithmetic of quadratic forms. Invent. Math.60, 193–248 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  26. [Y2] Yoshida, H.: On Siegel modular forms obtained from theta series. J. Reine Angew. Math.352, 184–219 (1984)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Siegfried Böcherer
    • 1
    • 2
  • Rainer Schulze-Pillot
    • 1
    • 2
  1. 1.Fakultät für Mathematik und InformatikUniversität MannheimMannheimFederal Republic of Germany
  2. 2.Mathematisches InstitutUniversität zu KölnKöln 41Federal Republic of Germany

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