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A Jacobi-Eisenstein series of weight two on congruence Jacobi subgroup

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Abstract

The specific aims of this paper are to define a Jacobi-Eisenstein series of weight two on congruence Jacobi subgroup and to compute its Fourier expansion coefficients in detail. To overcome the difficulties that the Jacobi-Eisenstein series of weight two is not convergent absolutely, we use the Hecke’s trick.

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References

  1. Choie Y. Correspondence among Eisenstein series E 2,1(τ, z), \( H_{\tfrac{3} {2}} \left( \tau \right) \) and E 2(τ). Manuscripta Math, 1997, 93: 177–187

    Article  MATH  MathSciNet  Google Scholar 

  2. Cohen H. Sums involving the values at negative integers of L functions of quadratic characters. Math Ann, 1975, 217: 271–285

    Article  MATH  MathSciNet  Google Scholar 

  3. Eichler M, Zagier D. The Theory of Jacobi Forms. Boston: Birkhäuser, 1985

    MATH  Google Scholar 

  4. Hirzebruch F, Zagier D. Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentpus. Invent Math, 1976, 36: 57–113

    Article  MATH  MathSciNet  Google Scholar 

  5. Lu H. Gauss’s Conjectures on the Quadratic Number Fields (in Chinese). Shanghai: Shanghai Scientific & Technical Publisher, 1994

    Google Scholar 

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Correspondence to HaiGang Zhou.

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Dedicated to Professor Wang Yuan on the Occasion of his 80th Birthday

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Lu, H., Zhou, H. A Jacobi-Eisenstein series of weight two on congruence Jacobi subgroup. Sci. China Math. 53, 2405–2410 (2010). https://doi.org/10.1007/s11425-010-4057-9

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  • DOI: https://doi.org/10.1007/s11425-010-4057-9

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