A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS

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...

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Bibliographic Details
Published inForum of mathematics. Sigma Vol. 8
Main Author BROWN, FRANCIS
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 2020
Subjects
11F03
11F67
11M3
11M32
81T30
Analytic functions
Integrals
Mathematical analysis
Modular construction
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2020.24