标题： 一种在代数框架内生成多元泽塔值形变的恒等式 显示英文标题

标题： An identity for generating series of deformations of multiple zeta values within an algebraic framework

摘要： 巴赫曼证明了一个恒等式，该恒等式通过艾森斯坦级数表达了麦克马洪推广的除数和生成级数$q$系列。麦克马洪的$q$系列可以被视为多重泽塔值$\zeta(2, 2, \ldots , 2)$的$q$类比，相差一个$1-q$的幂次。 基于这一观察，我们在一个代数框架内推广了巴赫曼的恒等式，并证明了一般性恒等式。作为副产品，我们得到了作者定义的多重泽塔值另一个变形的生成级数公式。在这个公式中，刘易斯和扎吉尔引入的类似周期函数作为艾森斯坦级数的对应物出现。 显示英文摘要

摘要： Bachmann proves an identity expressing the generating series of MacMahon's generalized sum-of-divisors $q$-series in terms of Eisenstein series. MacMahon's $q$-series can be regarded as a $q$-analogue of the multiple zeta value $\zeta(2, 2, \ldots , 2)$, up to a power of $1-q$. Based on this observation, we generalize Bachmann's identity within an algebraic framework and prove a general identity. As a byproduct, we obtain a formula for the generating series of another deformation of multiple zeta values defined by the author. In this formula, periodlike functions introduced by Lewis and Zagier appear as a counterpart of Eisenstein series.