A class of non-holomorphic modular forms II : equivariant iterated Eisenstein integrals

Understand

We introduce a new family of real analytic modular forms on the upper half plane.

• They are arguably the simplest class of `mixed' versions of modular forms of level one and are constructed out of real and imaginary parts of iterated integrals of holomorphic Eisenstein series.
• They form an algebra of functions satisfying many properties analogous to classical holomorphic modular forms.
• In particular, they admit expansions in $q, \overline{q}$ and $\log |q|$ involving only rational numbers and single-valued multiple zeta values.