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Iterated Shimura integrals. (English) Zbl 1215.11052
Summary: In this paper I continue the study of iterated integrals of modular forms and noncommutative modular symbols for $$\Gamma \subset \text{SL}(2,\mathbb Z)$$ started in [Iterated integrals of modular forms and noncommutative modular symbols. Prog. Math. 253, 565–597 (2006; Zbl 1184.11019)]. Main new results involve a description of the iterated Shimura cohomology and the image of the iterated Shimura cocycle class inside it. The concluding section of the paper contains a concise review of the classical modular symbols for $$\text{SL}(2)$$ and a discussion of open problems.

##### MSC:
 11F67 Special values of automorphic $$L$$-series, periods of automorphic forms, cohomology, modular symbols 11M55 Relations with noncommutative geometry 11G55 Polylogarithms and relations with $$K$$-theory 11M32 Multiple Dirichlet series and zeta functions and multizeta values
Zbl 1184.11019