发表机构
Addis Ababa University（亚的斯亚贝巴大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入分数伽马正则化泽塔核的变体，研究其解析性质与收敛性，证明其作为黎曼泽塔函数的形变，并在特定极限下插值到交替泽塔函数，同时提供狄利克雷级数表示。
AI 中文摘要
在本文中，我们引入并研究了一个特殊函数，称为分数伽马正则化泽塔核的一个变体，其中下不完全伽马函数出现在分子中，与分数超几何泽塔函数形成对比，后者中该函数出现在分母中。我们研究了其解析性质、收敛行为及其与黎曼泽塔函数的联系。我们推导出该函数作为黎曼泽塔函数的乘法修正的一种表示，并与已知的无零点区域和形变现象进行了比较。我们证明了该函数定义了黎曼泽塔函数的一种形变，并在特定极限下插值到交替泽塔函数。此外，我们提供了狄利克雷级数型的表示。最后，我们提出了未来工作的潜在扩展，包括函数方程和渐近分析。
英文摘要
In this paper, we introduce and study a special function, referred to as a variant of the fractional gamma-regularized zeta kernel, in which the lower incomplete gamma function appears in the numerator, contrasting with the fractional hypergeometric zeta function, where it appears in the denominator. We investigate its analytic properties, convergence behavior, and its connection to the Riemann zeta function. A representation is derived in terms of a multiplicative modification of the Riemann zeta function, and comparisons are made with known zero-free regions and deformation phenomena. We demonstrate that this function defines a deformation of the Riemann zeta function, which interpolates to the alternating zeta function in a specific limit. Additionally, a Dirichlet-type series representation is provided. Potential extensions, including a functional equation and asymptotic analysis, are proposed for future work.
Comments7 pages
