Special values of elliptic functions at points of the divisors of Jacobi forms

Choie, YoungJu; Kohnen, Winfried

doi:10.1090/S0002-9939-03-06945-4

Special values of elliptic functions at points of the divisors of Jacobi forms
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by YoungJu Choie and Winfried Kohnen PDF

Proc. Amer. Math. Soc. 131 (2003), 3309-3317 Request permission

Abstract:

The main result of the paper gives an explicit formula for the sum of the values of even order derivatives with respect to $z$ of the Weierstrass $\wp$-function $\wp (\tau ,z)$ for the lattice ${\mathbf Z}\tau \oplus {\mathbf Z}$ (where $\tau$ is in the upper half-plane) extended over the points in the divisor of $\phi (\tau ,\cdot )$ (where $\phi (\tau ,z)$ is a meromorphic Jacobi form) in terms of the coefficients of the Laurent expansion of $\phi (\tau ,z)$ around $z=0$.

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