Geodesic
A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS
Forum of Mathematics, Sigma, Tome 8 (2020)

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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. The first nontrivial functions in this class are real-analytic Eisenstein series. 
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     author = {FRANCIS BROWN},
     title = {A {CLASS} {OF} {NONHOLOMORPHIC} {MODULAR} {FORMS} {II:} {EQUIVARIANT} {ITERATED} {EISENSTEIN} {INTEGRALS}},
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FRANCIS BROWN. A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS. Forum of Mathematics, Sigma, Tome 8 (2020). doi: 10.1017/fms.2020.24

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