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Exact formula for Jacobi-Eisenstein series of square free discriminant lattice index
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In this paper we give an exact formula for the Fourier coefficients of the Jacobi-Eisenstein series of square free discriminant lattice index. For a special case the discriminant of lattice is prime we show that the Jacobi-Eisenstein series corresponds to a well known Eisenstein series of modular forms.
Abstract
In this paper we give an exact formula for the Fourier coefficients of the Jacobi-Eisenstein series of square free discriminant lattice index. For a special case the discriminant of lattice is prime we show that the Jacobi-Eisenstein series corresponds to a well known Eisenstein series of modular forms.
참고문헌 (7)
- A. Ajouz, "Hecke operators on Jacobi forms of lattice index and the relation to elliptic modular forms", Ph. D., pp.2015
- Jan Hendrik Bruinier, "On Borcherds products associated with lattices of prime discriminant", The Ramanujan Journal, 7(1, pp.3) (2003), 49~61[DOI]
- Jan Hendrik Bruinier, "Eisenstein series attached to lattices¶and modular forms on orthogonal groups", manuscripta mathematica, 106(4), pp.443~459 (2001), Springer Science and Business Media LLC[DOI]
- J. H. Conway, "Sphere Packings, Lattices and Groups" (1999), Springer-Verlag
- M. Eichler, "The theory of Jacobi forms" (1985), Birkhauser Boston, Inc
- A. Mocanu, "Poincare and Eisenstein series for Jacobi forms of lattice index", arXiv1712. 08174v2, ~ (2018)
- M. Woitalla, "Calculating the Fourier coecients of Jacobi-Eisenstein series", arXiv1705. 04595v2, ~ (2017)
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