论文标题
Euler Totient函数的概括
A Generalisation of Euler Totient Function
论文作者
论文摘要
Euler的基本功能，$φ（n）$，它计算了$ 0,1，\ dots，n-1 $的$ n $中的$ n/\ log \ log \ log \ log n $，modulo有一个明确的渐近下限。在本说明中，我们概括$φ$；给定一个不可约的整数多项式$ p $，我们定义了算术函数$φ_p（n）$，该函数计算$ p（0），p（1），\ dots，p（n-1）$之间的数量，这些数量与$ n $。我们还为$φ_p（n）$提供了渐近下限。
Euler's totient function, $φ(n)$, which counts how many of $0,1,\dots,n-1$ are coprime to $n$, has an explicit asymptotic lower bound of $n/\log \log n$, modulo some constant. In this note, we generalise $φ$; given an irreducible integer polynomial $P$, we define the arithmetic function $φ_P(n)$ that counts the amount of numbers among $P(0),P(1),\dots,P(n-1)$ that are coprime to $n$. We also provide an asymptotic lower bound for $φ_P(n)$.
