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Iterated integrals of modular forms and noncommutative modular symbols. (English) Zbl 1184.11019
Ginzburg, Victor (ed.), Algebraic geometry and number theory. In Honor of Vladimir Drinfeld’s 50th birthday. Basel: Birkhäuser (ISBN 978-0-8176-4471-0/hbk). Progress in Mathematics 253, 565-597 (2006).
From the text: This paper was inspired by two sources: the theory of multiple zeta values on the one hand [see D. Zagier, Prog. Math. 120, 497–512 (1994; Zbl 0822.11001)] and the theory of modular symbols and periods of cusp forms on the other. The main goal of this paper is to study properties of the iterated integrals of modular forms in the upper half-plane, possibly multiplied by $$z^{s-1}$$, along geodesics connecting two cusps. This setting generalizes simultaneously the theory of modular symbols and that of multiple zeta values.
For the entire collection see [Zbl 1113.00007].

MSC:
 11F67 Special values of automorphic $$L$$-series, periods of automorphic forms, cohomology, modular symbols 11M32 Multiple Dirichlet series and zeta functions and multizeta values 11G55 Polylogarithms and relations with $$K$$-theory
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