Generating function of multiple polylog of Hurwitz type
Generating function of multiple polylog of Hurwitz type
复制标题
DOI：
10.4153/s0008414x22000621
复制
发表时间：
2022-11
期刊：
影响因子：
--
通讯作者：
K. Ihara;Y. Kusunoki;Yayoi Nakamura;Hitomi Saeki
中科院分区：
文献类型：
--
作者：
K. Ihara;Y. Kusunoki;Yayoi Nakamura;Hitomi Saeki
摘要本文介绍了内插多重Hurwitz多元对数和内插多重Hurwitz zeta值。此外，我们还讨论了固定重量，深度和所有高度的polylog/zeta值之和的生成函数。函数用广义超几何函数表示。与Ohno和Zagier关于生成函数的开创性结果相比，我们的设置在三个方向上推广了结果，即，在一般高度，用t-插值，作为Hurwitz型。作为应用，通过将Hurwitz参数固定为有理数，给出了具有水平的多重zeta值的生成函数。
Abstract We introduce interpolated multiple Hurwitz polylogs and interpolated multiple Hurwitz zeta values. In addition, we discuss the generating functions for the sum of the polylogs/zeta values of fixed weight, depth, and all heights. The functions are expressed in terms of generalized hypergeometric functions. Compared with the pioneering results of Ohno and Zagier on the generating function, our setup generalizes the results in three directions, namely, at general heights, with a t-interpolation, and as a Hurwitz type. As an application, by fixing the Hurwitz parameter to rational numbers, the generating functions for multiple zeta values with level are given.