Antiderivatives of modular integrals and the Mellin transforms

초록

We study antiderivatives of modular integrals for the groups Γ0+(p) and their Mellin transforms where p∈{1,2,3}. In this paper, we show that these antiderivatives satisfy certain transformation laws involving logarithmic terms determined by rational period functions. Furthermore, we establish the analytic properties of the associated Mellin transform and derive its functional equation. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2026.

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