Commentarii Mathematici Helvetici

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Volume 81, Issue 2, 2006, pp. 481–494
DOI: 10.4171/CMH/60

Published online: 2006-06-30

Iterated integrals and higher order automorphic forms

Nikolaos Diamantis[1] and Ramesh Sreekantan[2]

(1) University of Nottingham, United Kingdom
(2) Tata Institute of Fundamental Research, Bombay, India

Higher order automorphic forms have recently been introduced to study important questions in number theory and mathematical physics. We investigate the connection between these functions and Chen's iterated integrals. Then using Chen's theory, we prove a structure theorem for automorphic forms of all orders. This allows us to define an analogue of a mixed Hodge structure on a space of higher order automorphic forms.

Keywords: Higher-order automorphic forms, Chen iterated integrals, mixed Hodge structures

Diamantis Nikolaos, Sreekantan Ramesh: Iterated integrals and higher order automorphic forms. Comment. Math. Helv. 81 (2006), 481-494. doi: 10.4171/CMH/60