Iterated integrals of modular forms and noncommutative modular symbols

By Yuri I. Manin. 2005

110 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d6927f0db1746ae5ccf6a2ce6bca39b421536d91

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Falko Dulat
2. Claude Duhr
3. Johannes Broedel
4. L. Tancredi
5. R. Hain
6. B. Penante
7. Gudrun Heinrich

In Discrete Mathematics and Combinatorics

1. R. Hain
2. B. Penante
3. L. Tancredi
4. Claude Duhr
5. Falko Dulat
6. Johannes Broedel

In Mathematical Physics

1. R. Hain
2. B. Penante
3. L. Tancredi
4. Claude Duhr
5. Falko Dulat
6. Johannes Broedel
7. S. Grushevsky
8. R. Pandharipande

Citations in the corpus

• The Hodge-de~Rham Theory of Modular Groups (2014, background): “VMHS associated to Modular Forms and their Period Maps This section considers three related topics: relative Higher albanese maps (which are related to period mappings of VMHS), Manin’s iterated Shimura integrals, and 14Here B2n is the 2nth Bernoulli number, ζ(s) is the Riemann zeta function and σk(”
• Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series (2018, methodology): “Closely related to eMPLs are iterated integrals of modular forms [73, 74], and it was indeed observed that they show up in Feynman integral computations [43, 65].”