arXiv subjects

Tianfang Qi

Publications and source records attributed to Tianfang Qi.

2 recordsLinked to original sources

arXiv2021

Multiple Mertens evaluations

The Mertens' first theorem gives us the following asymptotic formula \begin{equation*} \sum_{\substack{p\leq x\\ p~prime}}\frac{lnp}{p}=lnx+O(1), \end{equation*} and the Mertens' second theorem indicates that there exists a constant $B\approx 0.261$, named the Mertens constant, such that \begin{equation*} \sum_{\substack{p\leq x\\ p~prime}}\frac{1}{p}=ln(lnx)+B+O\left(\frac{1}{lnx}\right). \end{equation*} In this paper, by using the Abel summation formula and Dirichlet's hyperbola method, we extend them to multiple cases.

math.NT↗

arXiv2019

Ramanujan expansions of arithmetic functions of several variables over $\mathbb{F}_{q}[T]$

Let $\mathbb{A}=\mathbb{F}_{q}[T]$ be the polynomial ring over finite field $\mathbb{F}_{q}$, and $\mathbb{A}_{+}$ be the set of monic polynomials in $\mathbb{A}$. In this paper, we show that a large class of arithmetic functions in multi-variables over $\mathbb{A}_{+}$ can be expanded through the polynomial Ramanujan sums and the unitary polynomial Ramanujan sums. These are analogues of classical results over $\mathbb{N}$ by Winter, Delange and Tóth.

math.NT↗