Iterated integrals of modular forms and noncommutative modular symbols

  • Yuri I. Manin
Part of the Progress in Mathematics book series (PM, volume 253)


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.


Modular Form Eisenstein Series Formal Series Cusp Form Congruence Subgroup 
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© Birkhäuser Boston 2006

Authors and Affiliations

  • Yuri I. Manin
    • 1
    • 2
  1. 1.Max-Planck Institut für MathematikBonnGermany
  2. 2.Department of MathematicsNorthwestern UniversityEvanstonUSA

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