對於動機版山本積分的餘積公式

Abstract

亞歷山大·岡察洛夫證明了對於動機疊代積分的霍普夫代數中餘積之具體公式。山本積分是一種疊代積分的推廣，山本修司引入山本積分並給予多重ζ星值一種新的積分表示式。在本篇論文中，我們考慮動機版山本積分並推廣岡察洛夫的餘積公式至那些動機積分。作為範例，我們將計算一些特定形式的舒爾多重ζ值之餘積。

Goncharov proved an explicit formula for the coproduct in the Hopf algebra of motivic iterated integrals. Yamamoto introduced Yamamoto’s integral which generalizes iterated integrals and gave a new integral expression for multiple zeta star values using Yamamoto’s integral. In this paper, we consider the motivic version of Yamamoto’s integral and generalize Goncharov’s coproduct formula to those motivic integrals. As an example, we will compute the coproduct of a certain type of Schur multiple zeta values.