On the Rankin-Selberg method for higher genus string amplitudes

@article{Florakis2016OnTR,
  title={On the Rankin-Selberg method for higher genus string amplitudes},
  author={Ioannis Florakis and Boris Pioline},
  journal={Communications in Number Theory and Physics},
  year={2016},
  volume={11},
  pages={337-404}
}
Closed string amplitudes at genus $h\leq 3$ are given by integrals of Siegel modular functions on a fundamental domain of the Siegel upper half-plane. When the integrand is of rapid decay near the cusps, the integral can be computed by the Rankin-Selberg method, which consists of inserting an Eisenstein series $E_h(s)$ in the integrand, computing the integral by the orbit method, and finally extracting the residue at a suitable value of $s$. String amplitudes, however, typically involve… 

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