A single theta-lift construction generates both two-loop modular graph functions and S-dual modular functions as rational combinations of generalised Eisenstein series with all cusp-form L-values cancelling.
Whittaker Fourier type solutions to differential equations arising from string theory
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abstract
In this article, we find the full Fourier expansion for the generalized non-holomorphic Eisenstein series for certain values of parameters. We give a connection of the boundary condition on such Fourier series with convolution formulas on the divisor functions. Additionally, we discuss a possible relation with the differential Galois theory.
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Modular Features of Superstring Scattering Amplitudes: Generalised Eisenstein Series and Theta Lifts
A single theta-lift construction generates both two-loop modular graph functions and S-dual modular functions as rational combinations of generalised Eisenstein series with all cusp-form L-values cancelling.