科研之友
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摘要
We start with a series F = Sigma(r >>-infinity) f(r) . pi(r) with indeterminate pi and where the coefficients f(r) = fr (z(1),..., z(n)) are holomorphic functions defined on an open neighborhood of the closed polydisc (D) over bar (n) = {( z(1),...,z(n)); | zi | <= 1}. Integrating the coefficients of this series on the n-dimensional real cube [0, 1](n) yields a Laurent series integral(n)([0,1]) F. When F is algebraic we say that integral(n)([0,1]) F is a series of periods. In this article, our goal is to determine the algebraic series F such that integral(n)([0,1]) 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 modified form.
- 出版日期2015-5
