A class of non-holomorphic modular forms I

By F. Brown. 2017

95 citations recorded by the source corpus.

This introductory paper studies a class of real analytic functions on the upper half plane satisfying a certain modular transformation property. They are not eigenfunctions of the Laplacian and are quite distinct from Maass forms. These functions are modular equivariant versions of real and imaginary parts of iterated integrals of holomorphic modular forms and are modular analogues of single-valued polylogarithms. The coefficients of these functions in a suitable power series expansion are periods. They are related both to mixed motives (iterated extensions of pure motives of classical modular forms) and to the modular graph functions arising in genus one string perturbation theory.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/968ab1f05a47a06b7ed90ffc9f51f5de7590484b

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In Algebra and Number Theory

1. F. Brown
2. Erik Panzer
3. Claude Duhr
4. Oliver Schnetz
5. Gudrun Heinrich
6. Falko Dulat
7. Thomas Willwacher
8. S. Stieberger

In Mathematical Physics

1. F. Brown
2. Erik Panzer
3. Oliver Schnetz
4. Gudrun Heinrich
5. P. Baikov
6. Mikhail V. Kompaniets
7. K. Chetyrkin

Citations in the corpus

• A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS (2017, methodology): “Notations and background on the class of functions M We recall some notations and background from [6, 36].”