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High Energy Physics - Theory, hep-th
Abstract:
In this note we study $SL(2,\mathbb{Z})$-invariant functions such as modular
graph functions or coefficient functions of higher derivative corrections in
type IIB string theory. The functions solve inhomogeneous Laplace equations and
we choose to represent them as Poincar\'e series. In this way we can combine
different methods for asymptotic expansions and obtain the perturbative and
non-perturbative contributions to their zero Fourier modes. In the case of the
higher derivative corrections, these terms have an interpretation in terms of
perturbative string loop effects and pairs of instantons/anti-instantons.
