Skip to main content
SpringerLink
Log in

Zur berechnung des ranges der schar der elliptischen spitzenformen

  • Published:
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literatur

  1. S. Akiyama, Selberg trace formula for odd weight (preprint).

  2. U. Christian, Siegeische Modulformen und Integralgleichungen. Math. Zeitschr.101 (1967), 299–305.

    Article  MATH  MathSciNet  Google Scholar 

  3. U. Christian, Über die Anzahl der Spitzen Siegelscher Modulgruppen. Abh. Math. Sem. Univ. Hamburg32 (1968), 55–60.

    Article  MATH  MathSciNet  Google Scholar 

  4. U. Christian, Hilbert-Siegelsche Modulformen und Integralgleichungen. Monatsh. f. Math.72 (1968), 412–418.

    Article  MATH  MathSciNet  Google Scholar 

  5. U. Christian, Untersuchung einer Poincaréschen Reihe, I. J. reine angew. Math.233 (1968), 37–88.

    MATH  MathSciNet  Google Scholar 

  6. U. Christian, Untersuchung einer Poincaréschen Reihe, II. J. reine angew. Math.237 (1969), 12–25.

    MATH  MathSciNet  Google Scholar 

  7. U. Christian, Berechnung des Ranges der Schar der Spitzenformen zur Modulgruppe zweiten Grades und Stufe q > 2. J. reine angew. Math.277 (1975), 130–154.

    MATH  MathSciNet  Google Scholar 

  8. U. Christian, Zur Berechnung des Ranges der Schar der Spitzenformen zur Modulgruppe zweiten Grades und Stufe q > 2. J. reine angew. Math.296 (1977), 108–118.

    MATH  MathSciNet  Google Scholar 

  9. U. Christian, Siegeische Modulfunktionen. Vorlesungsausarbeitung, Göttingen 1980/81.

  10. U. Christian, On the analytic continuation of Eisenstein series for Siegel’s modular group of degreen. Monatsh. f. Math.96 (1983), 101–106.

    Article  MATH  MathSciNet  Google Scholar 

  11. U. Christian, Über die analytische Fortsetzung gewisser Poincaréscher Reihen zu elliptischen Modulgruppen. Tôhoku Math. J.

  12. U. Christian, Über gewisse Poincarésche Reihen zu elliptischen Modulgruppen. Manuscrip-ta math.59 (1987), 423–440.

    Article  MATH  MathSciNet  Google Scholar 

  13. U. Christian, Untersuchung Selbergscher Zetafunktionen J. Math. Soc. Japan41, No 3, (1989).

  14. U. Christian, Zur Theorie Selbergscher Zetafunktionen. Arch. d. Math.52 (1989).

  15. L. D. Faddeev, Expansion in Eigenfunctions of the Laplace operator on the fundamental domain of a discrete group on the Lobacevskii plane. Trans. Moscow. Math. Soc.17 (1967), 357–386.

    MathSciNet  Google Scholar 

  16. K.-B. Gundlach, Über die Darstellung der ganzen Spitzenformen zu den Idealstufen der Hilbertschen Modulgruppe und die Abschätzung ihrer Fourierkoeffizienten. Acta math.92 (1954), 309–345.

    Article  MATH  MathSciNet  Google Scholar 

  17. R. C. Gunning, Lectures on modular forms. Princeton Univ. Press 1962.

  18. K. Hashimoto, The dimension of the spaces of cusp forms on Siegel upper half plane of degree two (I). J. Fac. Sei. Univ. Tokyo30 (1983), 403–488.

    MATH  MathSciNet  Google Scholar 

  19. K. Hashimoto, The dimension of the spaces of cusp forms on Siegel upper half plane of degree two (II). Math. Ann.266 (1984), 539–559.

    Article  MATH  MathSciNet  Google Scholar 

  20. K. Hashimoto, On the first, second and third asymptotic formulas for the dimension of the space of Siegel modular forms of degreen. Sé minaire de théorie des nombres de Paris 1982/83, Birkhäuser Verlag 1984.

  21. K. Hashimoto and T. Ibukiyama, On relations of dimensions of automorphic forms ofSp(2, R) and its compact twistSp(2). Advanced Studies in pure Math.17. Automorphic forms and number theory, 31 -102, 1985.

  22. Hejhal, D. A. The Selberg trace formula forPSL(2, R). I. Springer Lecture Notes in Math. 548. II. Springer Lecture Notes in Math. 1001.

  23. T. Hiramatsu, Eichler classes attached to automorphic forms of dimension —1. Osaka J.Math.3 (1966), 39–48.

    MATH  MathSciNet  Google Scholar 

  24. T. Hiramatsu, On automorphic forms of weight one. I. Mathematics seminar notes8 (1980), 173–179.

    MATH  MathSciNet  Google Scholar 

  25. T. Hiramatsu, On automorphic forms of weight one. III. The Selberg eigenspace for discontinuous groups of finite type (preprint).

  26. T. Hiramatsu, On some dimension formula for automorphic forms of weight one. I. Nagoya Math. J.85 (1982), 213–221. II. Nagoya Math. J.105 (1987), 169-186.

    MATH  MathSciNet  Google Scholar 

  27. T. Hiramatsu, Theory of automorphic forms of weight 1. Advanced Studies in pure Math.13 (1988), 503–584.

    MathSciNet  Google Scholar 

  28. T. Hiramatsu, A formula for the dimension of spaces of cusp forms of weight 1 (preprint).

  29. T. Hiramatsu and S. Akiyama, On some dimension formula for automorphic forms of weight one, III (preprint).

  30. T. Hiramatsu andY. Mimura, On automorphic forms of weight one, II. Math, seminar notes9 (1981), 259–267.

    MATH  MathSciNet  Google Scholar 

  31. H. Ishikawa andY. Tanigawa, The dimension formula of the space of cusp forms of weight one for г0(O). Proc. Japan Acad.63 (1987), 31–34, und preprint.

    MATH  MathSciNet  Google Scholar 

  32. T. Kubota, Elementary theory of Eisenstein series. Kodansha, Tokyo, John Wiley, New York, London, Sydney, Toronto.

  33. N. V. Kuznetsov, Convolution of the Fourier coefficients of the Eisenstein-Maass series. J. Soviet Math.29 (1985), 1131–1159.

    Article  MATH  Google Scholar 

  34. S. Lang,SL 2(R). Addison-Wesley Publ. Comp.

  35. W. Magnus und F. Oberhettinger, Formeln und Sätze für die speziellen Funktionen der Mathematischen Physik, 2. Auflage, Springer Verlag 1948.

  36. H. Maass, Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen. Math. Ann.121 (1949), 141–183.

    Article  MATH  MathSciNet  Google Scholar 

  37. H. Maass, Lectures on modular functions of one complex variable. Lecture Notes, Tata Institute of Fundamental Research, Bombay 1964, revised 1983.

  38. Y. Morita, An explicit formula for the dimension of spaces of Siegel modular forms of degree two. Journal of the Faculty of Science, the University of Tokyo, Sec. IA21 (1974), 167–248.

    MATH  Google Scholar 

  39. H. Petersson, Ein Summationsverfahren für die Poincaréschen Reihen von der Dimension (-2) zu den hyperbolischen Fixpunktpaaren. Math. Z.49 (1944), 441–496.

    Article  MATH  MathSciNet  Google Scholar 

  40. H. Petersson, Über Eisensteinsche Reihen der Dimension —1. Comm. Math. Helv.31 (1956), 111–144.

    Article  MATH  MathSciNet  Google Scholar 

  41. W. Roelcke, Über die Wellengleichung bei Grenzkreisgruppen erster Art. Sitzungsber. Heidelberger Akad. Wiss. 161–267, 1956.

  42. W. Roelcke, Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. I. Math. Ann.167 (1966), 292–337. II. Math. Ann.168 (1967), 261-324.

    Article  MathSciNet  Google Scholar 

  43. B. Schoeneberg, Elliptic modular functions, Springei-Verlag 1974.

  44. A. Selberg, Harmonic analysis. Vorlesungsausarbeitung, Göttingen 1954.

    Google Scholar 

  45. A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series. J. Indian Math. Soc.20 (1956), 47–87.

    MATH  MathSciNet  Google Scholar 

  46. J. P. Serre, Modular forms of weight one and Galois representations. Algebraic number fields.A. Frö hlich (edit.) Academic Press, London 1977.

    Google Scholar 

  47. H. Shimizu, On discontinuous groups operating on the product of the upper half planes. Annals of Mathematics77 (1963), 33–71.

    Article  MathSciNet  Google Scholar 

  48. H. Shimizu, A remark on the Hilbert modular forms of weight 1. Math. Ann.265 (1983), 457–472.

    Article  MATH  MathSciNet  Google Scholar 

  49. R. Tsushima, A formula for the dimension of spaces of Siegel cusp forms for degree three. Amer. J. Math.102 (1980), 937–977.

    Article  MATH  MathSciNet  Google Scholar 

  50. R. Tsushima, On the spaces of Siegel cusp forms of degree two. Amer. J. Math.104 (1981), 843–885.

    Article  MathSciNet  Google Scholar 

  51. R. Tsushima, An explicit dimension formula for the spaces of generalized automorphic forms with respect toSp(2, Z). Proc. Japan Acad.59 (1983), 139–142, und preprint.

    MATH  MathSciNet  Google Scholar 

  52. R. Tsushima, The spaces of Siegel cusp forms of degree two and the representation ofSp(2, Fp). Proc. Japan Acad.60 (1984), 209–211.

    Article  MATH  MathSciNet  Google Scholar 

  53. A. B. Venkov, Spectral theory of automorphic functions, the Selberg zetafunction and some problems of analytic number theory and mathematical physics. Russian Math. Surveys34 (1979), 3, 79–153.

    Article  MATH  MathSciNet  Google Scholar 

  54. A. B. Venkov, Spectral theory of automorphic functions. Proc. of the Steklov Institute of Math.153,1981.

  55. E. T. Whittaker and G. N. Watson, A course of modern analysis. Cambridge Univ. Press 1927.

  56. T. Yamasaki, On Siegel modular forms of degree two. Amer. J. Math.98 (1973), 39–53.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut der Georg-August-Universität, Bunsenstra\e 3-5, D-3400 Göttingen, Deutschland

    U. Christian

Authors
  1. U. Christian
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Christian, U. Zur berechnung des ranges der schar der elliptischen spitzenformen. Abh.Math.Semin.Univ.Hambg. 59, 61–79 (1989). https://doi.org/10.1007/BF02942316

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02942316

Search

Navigation