The distribution of Manin's iterated integrals of modular forms
Nils Matthes, Morten S. Risager
TL;DR
This paper investigates the asymptotic distribution of Manin's iterated integrals of modular forms, providing explicit moment calculations and revealing non-uniqueness in distributions for integrals of length three or more.
Contribution
It determines the asymptotic distribution of Manin's iterated integrals of length up to 2 and computes all moments for all lengths, highlighting non-uniqueness for lengths at least 3.
Findings
Asymptotic distribution determined for length ≤ 2
All moments computed for all lengths
Moments do not uniquely determine distribution for length ≥ 3
Abstract
We determine the asymptotic distribution of Manin's iterated integrals of length at most 2. For all lengths we compute all the asymptotic moments. We show that if the length is at least 3 these moments do in general not determine a unique distribution.
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Identities · Advanced Algebra and Geometry