Torseurs associates a certain relations algebriques entre polyzetas aux racines de l'unite
Torseurs associes a certaines relations algebriques entre polyzetas aux racines de l'unite
摘要：
我们在这份说明中描述的torsor结构所产生的仿射计划所定义的一个系统的合理代数关系polyzetas在根的单位（值的超对数函数的固定有限群的复根的单位）。当这个群被减少到1时，我们称这些数为polyzeta。它们将黎曼ζ函数的值推广为奇数正整数，也称为MZVs、多重zeta、多重调和级数或Euler/Zagier和。我们相信，我们在这里考虑的关系涵盖了它们之间的所有代数关系。在这种情况下，这些关系背后的torsor结构应该与作用于结合子的Grothendieck-Teichmueller群构成的Drinfeld torsor相同。从绝对伽罗瓦群在射影直线上的作用导出了一般情况下的公式。这是一个很容易的结果torsor结构的代数定义的这些关系是一个多项式代数。这是J. Ecalle在polyzetas案中首先提出的。
英文摘要：
We describe in this note a torsor structure arising on the affine scheme defined by a system of rationnal algebraic relations between polyzetas at roots of unity (values of hyperlogarithmic functions on a fixed finite group of complex roots of unity). When this group is reduced to 1, we call these numbers the polyzetas. They generalize the values of the Riemann zeta function at odd positive integers and are also called MZVs, multizetas, multiple harmonic series or Euler/Zagier sums. It is believed that the relations we consider here span all algebraic relations between them. The torsor structure underlying these relations should in that case be se same as Drinfeld's torsor made of the Grothendieck- Teichmueller group acting on associators. The formulas for the general case are derived from the action of the absolute Galois group on the projective line minus finitely many points. It is an easy consequence of the torsor structure that the algebra defined by these relations is a polynomial algebra. This was stated first by J. Ecalle in the polyzetas case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
