Iterated integrals of modular forms and noncommutative modular symbols
Yu. I. Manin
TL;DR
This paper investigates the properties of iterated integrals of modular forms along geodesics, generalizing modular symbols and multiple zeta values, to deepen understanding of their mathematical structure.
Contribution
It introduces a framework for studying iterated integrals of modular forms, extending the theory of modular symbols and connecting to multiple zeta values.
Findings
Established properties of iterated integrals in this setting
Connected modular symbols with multiple zeta values
Provided new insights into the structure of these integrals
Abstract
The main goal of this paper is to study properties of the iterated integrals of modular forms in the upper halfplane, eventually multiplied by , along geodesics connecting two cusps. This setting generalizes simultaneously the theory of modular symbols and that of multiple zeta values
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Algebra and Geometry · Analytic Number Theory Research