Une version relative de la conjecture des périodes de Kontsevich-Zagier, by Joseph Ayoub

We start with a Laurent series F whose coefficients are given by holomorphic functions on an open neighborhood of the closed polydisc of radius 1 and dimension n. We assume furthermore that F is algebraic in an appropriate sense. Integrating the coefficients on the real unit cube of dimension n yields a Laurent series with complex coefficients. We are interested in knowing when the resulting series is zero. Our main result is reminiscent to the Kontsevich-Zagier conjecture on periods in a modified form.


Joseph Ayoub <joseph.ayoub@math.uzh.ch>