arXiv subjects

Yong-Guo Shi

Publications and source records attributed to Yong-Guo Shi.

4 recordsLinked to original sources

arXiv2024

Some reciprocity formulas for generalized Dedekind-Rademacher sums

In this paper, we study the generalized Dedekind-Rademacher sums considered by Hall, Wilson and Zagier. We establish a formula for the products of two Bernoulli functions. The proof relies on Parseval's formula, Hurwitz's formula, and Lerch's functional equation. The result leads to reciprocity formulas for some generalizations of the classical Dedekind sums. In particular, it is shown that Carlitz's, Berndt's, Hall and Wilson's reciprocity theorems are deduced as special cases.

math.NT↗

arXiv2023

The asymptotic power series of three kinds of sequences

We present a general method to obtain asymptotic power series for three kinds of sequences. And we give recurrence relations for determining the coefficients of asymptotic power series for these sequences. As applications, we show how these theoretical results can be used to deduce approximation formulas for some well-known sequences and some integrals with a parameter.

math.CA↗

arXiv2020

Single-valley-extended solutions with platforms of FKS equation

The Feigenbaum-Kadanoff-Shenker (FKS) equation is a nonlinear iterative functional equation, which characterizes the quasiperiodic route to chaos for circle maps. Instead of FKS equation, we put forward the second type of FKS equation. We use the iterative construction method to obtain a new kind of continuous solutions with platforms for this functional equation. We show some properties of these continuous solutions, and give one relationship of some solutions between FKS equation and the second type of FKS equation.

math.DS↗

arXiv2019

Conjugacy problem of strictly monotone maps with only one jump discontinuity

The conjugacy problem is one of the central questions in iteration theory. As far as we, for discontinuous strictly monotone maps there is no complete result. In this paper, we investigate the conjugacy problem of strictly monotone maps with only one jump discontinuity. We give some sufficient and necessary conditions for the conjugacy relationship. And we present some methods to construct all conjugacies. Furthermore, we present the conditions to guarantee $C^1$ smoothness of these conjugacies.

math.DS↗