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The dimension of the space of Siegel–Eisenstein series of weight one

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Abstract

In general, it is difficult to determine the dimension of the space of Siegel modular forms of low weights. In particular, the dimensions of the spaces of cusp forms are known in only a few cases. In this paper, we calculate the dimension of the space of Siegel–Eisenstein series of weight 1, which is a certain subspace of a complement of the space of cusp forms.

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References

  1. Andrianov, A.N.: Quadratic forms and Hecke operators. Grundl. math. Wiss. vol. 286. Springer, Heidelberg (1987)

  2. Freitag E. (1975). Holomorphe Differentialformen zu Kongruenzgruppen der Siegelschen Modulgruppe. Invent. Math. 30: 181–196

    Article  MATH  MathSciNet  Google Scholar 

  3. Freitag E. (1977). Die Invarianz gewisser von Thetareihen erzeugter Vektorräume unter Heckeoperatoren. Math. Z. 156(2): 141–155

    Article  MATH  MathSciNet  Google Scholar 

  4. Gunji K. (2004). On the graded ring of Siegel modular forms of degree 2, level 3. J. Math. Soc. Japan 6(2): 375–403

    Article  MathSciNet  Google Scholar 

  5. Hecke E. (1927). Theorie der Eisensteinschen Reihen höherer Stufe und ihre Anwendung auf Funktionentheorie und Arithmetik. Abh. Math. Sem. Univ. Hamburg 5: 199–224

    Article  MATH  Google Scholar 

  6. Hecke, E.: Mathematische Werke. Göttingen Vandenhoeck & Ruprecht pp 461–486 (1970)

  7. Li J.-S. (1996). On the dimensions of spaces of Siegel modular forms of weight one. Geometric Funct. Anal. 6(3): 512–555

    Article  MATH  Google Scholar 

  8. Resnikoff H.L. (1975). Automorphic forms of singular weight are singular forms. Math. Ann. 215: 173–193

    Article  MATH  MathSciNet  Google Scholar 

  9. Schoeneberg, B.: Elliptic Modular Functions. Grundle. math. Wiss. vol. 203, Springer, Heidelberg (1974)

  10. Serre J.P. (1977). Linear Representations of Finite Groups. Graduate Texts in Mathematics, 42. Springer, Heidelberg

    Google Scholar 

  11. Srinivasan B. (1968). The character of the finite symplectic group Sp(4, q). Trans. Am. Math. Soc. 131: 488–525

    Article  MATH  Google Scholar 

  12. Washington, L.C.: Introduction to Cyclotomic Fields. 2nd edn. Graduate Texts in Mathematics, vol. 83. Springer, Heidelberg (1997)

  13. Weissauer R. (1992). Modular forms of genus 2 and weight 1. Math. Z. 210: 91–96

    Article  MATH  MathSciNet  Google Scholar 

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  1. Graduate School of Mathematical Science, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

    Keiichi Gunji

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  1. Keiichi Gunji
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Correspondence to Keiichi Gunji.

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Gunji, K. The dimension of the space of Siegel–Eisenstein series of weight one. Math. Z. 260, 187–201 (2008). https://doi.org/10.1007/s00209-007-0269-2

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  • DOI: https://doi.org/10.1007/s00209-007-0269-2

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