论文标题
关于Dirichlet字符的Menon型身份和GCD函数的概括
A Menon-type Identity concerning Dirichlet characters and a generalization of the gcd function
论文作者
论文摘要
Menon的身份是涉及GCD总和和Euler Toctient函数$ ϕ $的经典身份。在最近的一篇论文中，Zhao和Cao得出了Menon-Type身份$ \ sum \ limits _ {\ setack {k = 1}}}}^{n}^{n}（k-1，n）χ（k）= ϕ（k）= ϕ（n）τ（\ frac {n）我们得出了类似于此替换GCD的身份。我们还表明，如果使用我们在此处采用的方法，则可以改善Zhao-Cao身份的一些参数。
Menon's identity is a classical identity involving gcd sums and the Euler totient function $ϕ$. In a recent paper, Zhao and Cao derived the Menon-type identity $\sum\limits_{\substack{k=1}}^{n}(k-1,n)χ(k) = ϕ(n)τ(\frac{n}{d})$, where $χ$ is a Dirichlet character mod $n$ with conductor $d$. We derive an identity similar to this replacing gcd with a generalization it. We also show that some of the arguments used in the derivation of Zhao-Cao identity can be improved if one uses the method we employ here.
