Proves conjectural reformulation of motivic coaction and single-valued maps via zeta generators for multiple polylogarithms at genus zero on the Riemann sphere.
A class of non-holomorphic modular forms II : equivariant iterated Eisenstein integrals
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
abstract
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 non-trivial functions in this class are real analytic Eisenstein series.
citation-role summary
background 1
citation-polarity summary
verdicts
UNVERDICTED 3roles
background 1polarities
background 1representative citing papers
Defines L-functions for real-analytic modular forms and constructs period polynomial analogues for modular iterated integrals.
Proposes motivic coaction formulae for genus-one iterated integrals over holomorphic Eisenstein series using zeta generators, verifies expected coaction properties, and deduces f-alphabet decompositions of multiple modular values.
citing papers explorer
-
Deriving motivic coactions and single-valued maps at genus zero from zeta generators
Proves conjectural reformulation of motivic coaction and single-valued maps via zeta generators for multiple polylogarithms at genus zero on the Riemann sphere.
-
Period functions associated to real-analytic modular forms
Defines L-functions for real-analytic modular forms and constructs period polynomial analogues for modular iterated integrals.
-
Towards Motivic Coactions at Genus One from Zeta Generators
Proposes motivic coaction formulae for genus-one iterated integrals over holomorphic Eisenstein series using zeta generators, verifies expected coaction properties, and deduces f-alphabet decompositions of multiple modular values.