Equilibrium point of Green’s function for the annulus and Eisenstein series

Sebbar, Ahmed; Falliero, Thérèse

doi:10.1090/S0002-9939-06-08353-5

Equilibrium point of Green’s function for the annulus and Eisenstein series
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by Ahmed Sebbar and Thérèse Falliero PDF

Proc. Amer. Math. Soc. 135 (2007), 313-328 Request permission

Abstract:

We study the motion of the equilibrium point of Green’s function and give an explicit parametrization of the unique zero of the Bergman kernel of the annulus. This problem is reduced to solving the equation $\wp (z,\tau )= -\frac {\pi ^2}{3}E_2(\tau )$, where $E_2(\tau )$ is the usual Eisenstein series.

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