# Period functions associated to real-analytic modular forms

## TL;DR

This paper introduces L-functions for real-analytic modular forms, explores their properties, and constructs period polynomials, especially for modular iterated integrals, advancing understanding of their analytic and algebraic structures.

## Contribution

It defines L-functions for a new class of real-analytic modular forms and constructs associated period polynomials, extending classical theories.

## Key findings

- Established main properties of the L-functions.
- Constructed period polynomials for special cases.
- Extended classical modular form theories to real-analytic cases.

## Abstract

We define L-functions for the class of real-analytic modular forms recently introduced by F. Brown. We establish their main properties and construct the analogue of period polynomial in cases of special interest, including those of modular iterated integrals.