Period functions associated to real-analytic modular forms (Q2214913)

The authors define \(L\)-functions for real-analytic modular forms for the group \(\operatorname{SL}_2(\mathbb Z)\) which have at most exponential growth at the cusp \(\infty\). If \(f\) is a modular integral in the sense of \textit{F. Brown} [Res. Math. Sci. 5, No. 3, Paper No. 34, 36 p. (2018; Zbl 1440.11071)], then the authors define its period function and prove that its coefficients can be expressed in terms of special \(L\)-values of \(f\). For weakly holomorphic cusp forms, the authors also prove an analogue of Manin's period theorem [\textit{Yu. I. Manin}, Mat. Sb., Nov. Ser. 92(134), 378--401 (1973; Zbl 0293.14007)]. It should be mentioned that, independently, Brown has introduced \(L\)-functions of modular iterated integrals of Eisenstein series [\textit{F. Brown}, Forum Math. Sigma 8, Paper No. 31, 62 p. (2020; Zbl 1452.11054)].