Abstract
We start with a series F = P r1 fr $ r with indeterminate $ and where the coecients fr = fr(z1;:::;zn) are holomorphic functions dened on an open neighborhood of the closed polydisc D n =f(z1;:::;zn);jzij 1g. Integrating the coecients of this series on the n-dimensional real cube [0; 1] n yields a Laurent series R [0;1]n F . When F is algebraic we say that R [0;1]n F is a series of periods. In this article, our goal is to determine the algebraic series F such that R [0;1]n F is zero. In principle, this gives informations on the transcendence properties of series of periods. Our main result is reminiscent to the Kontsevich-Zagier conjecture on periods in a modied form.
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