arXiv subjects

Joshua Pimm

Publications and source records attributed to Joshua Pimm.

2 recordsLinked to original sources

arXiv2025

Summation Formulas for Harmonic Maass Forms

In a previous work (arXiv:2505.05574), a summation formula for harmonic Maass forms of polynomial growth was established. In this note, we use the theory of $L$-series of harmonic Maass forms to state and prove a summation formula for such forms without any restrictions on their growth. We deduce a summation formula for the partition function. We further employ the same theory to derive a result on classical modular forms, namely, a summation formula and the asymptotics of a Riesz sum attached to a cusp form.

math.NT↗

arXiv2023

Real-analytic modular forms for $\Gamma_0(N)$ and their $L$-series

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 equation and converse theorem. We also discuss examples of such forms, including real analytic Eisenstein series and modular iterated integrals of higher level. We focus on the $L$-series for a class of forms including Francis Brown's length-one modular iterated integrals $\mathcal{MI}^!_1$.

math.NT↗