Title: Koba-Nielsen local zeta functions, convex subsets, and generalized Selberg-Mehta-Macdonald and Dotsenko-Fateev-like integrals Show Chinese title

Title: 科巴-尼尔森局部zeta函数，凸子集，以及广义的塞尔伯格-梅塔-麦克唐纳和多琴科-法捷耶夫类似积分

Abstract: The Koba-Nielsen local zeta functions are integrals depending on several complex parameters, used to regularize the Koba-Nielsen string amplitudes. These integrals are convergent and admit meromorphic continuations in the complex parameters. In the original case, the integration is carried out on the n-dimensional Euclidean space. In this work, the integration is over a variety of (bounded or unbounded) convex subsets; the resulting integrals also admit meromorphic continuations in the complex parameters. We describe the meromorphic continuation's polar locus explicitly, using the technique of embedded resolution. This result can be reinterpreted as saying that the meromorphic continuations are weighted sums of Gamma functions, evaluated at linear combinations of the complex parameters, where the weights are holomorphic functions. The integrals announced in the title of this paper occur as a particular case of these new Koba-Nielsen local zeta functions, or of a further generalization to arbitrary hyperplane arrangements. Show Chinese abstract

Abstract: Koba-Nielsen局部zeta函数是依赖于多个复参数的积分，用于正则化Koba-Nielsen弦振幅。 这些积分是收敛的，并且在复参数中可以进行亚纯延拓。 在原始情况下，积分是在n维欧几里得空间上进行的。 在本工作中，积分是在各种（有界或无界）凸子集上进行的；所得积分同样可以在复参数中进行亚纯延拓。 我们使用嵌入解的方法，明确描述了亚纯延拓的极点位置。 这个结果可以重新解释为：亚纯延拓是Gamma函数的加权和，这些Gamma函数在复参数的线性组合上进行求值，其中权重是全纯函数。 本文标题中宣布的积分是这些新的Koba-Nielsen局部zeta函数的一个特例，或者是对任意超平面排列的进一步推广。