Real-analytic modular forms for ${\Gamma }_0(N)$ and their $L$-series

Joshua Drewitt, Joshua Pimm

We introduce an $L$-series associated to real-analytic modular forms which transform with weight $(r,s)\in {\mathbb{Z}}^2$ under ${\Gamma }_0(N)$. These $L$-series satisfy a functional equati…