对各类展式的误差和函数的研究从21世纪初就开始了,研究人员不断深入探讨其各种性质,如连续性、周期性、有界性、介值性等,同时给出函数图像的Hausdorff维数。在本文中,我们将探讨Hurwitz连分数的误差和函数,提出一些相关的性质,并研究...对各类展式的误差和函数的研究从21世纪初就开始了,研究人员不断深入探讨其各种性质,如连续性、周期性、有界性、介值性等,同时给出函数图像的Hausdorff维数。在本文中,我们将探讨Hurwitz连分数的误差和函数,提出一些相关的性质,并研究其图像。The study of error-sum functions of expansions has been ongoing since the beginning of the 21st century, and researchers have been delving into various properties such as continuity, periodicity, boundedness, median, etc., along with giving the Hausdorff dimension of the graphs of the functions. In this paper, we will explore the error-sum function of Hurwitz continued fractions, present some related properties, and study their graphs.展开更多
In this paper,we study the generalized Dedekind Rademacher sums considered by Hall,Wilson and Zagier.We establish a new formula for the products of two Bernoulli functions by using Parseval's formula,Hurwitz's...In this paper,we study the generalized Dedekind Rademacher sums considered by Hall,Wilson and Zagier.We establish a new formula for the products of two Bernoulli functions by using Parseval's formula,Hurwitz's formula and Lerch's functional equation.As applications of the result,some well-known reciprocity formulas are deduced as special cases.展开更多
文摘对各类展式的误差和函数的研究从21世纪初就开始了,研究人员不断深入探讨其各种性质,如连续性、周期性、有界性、介值性等,同时给出函数图像的Hausdorff维数。在本文中,我们将探讨Hurwitz连分数的误差和函数,提出一些相关的性质,并研究其图像。The study of error-sum functions of expansions has been ongoing since the beginning of the 21st century, and researchers have been delving into various properties such as continuity, periodicity, boundedness, median, etc., along with giving the Hausdorff dimension of the graphs of the functions. In this paper, we will explore the error-sum function of Hurwitz continued fractions, present some related properties, and study their graphs.
基金Supported by the Natural Science Foundation of Sichuan Province(No.2023NSFSC0065)。
文摘In this paper,we study the generalized Dedekind Rademacher sums considered by Hall,Wilson and Zagier.We establish a new formula for the products of two Bernoulli functions by using Parseval's formula,Hurwitz's formula and Lerch's functional equation.As applications of the result,some well-known reciprocity formulas are deduced as special cases.
