Let $n = p_{1} p_{2} cdots p_{r}$ be a product of $r$ prime numbers which arenot necessarily different. We define then an arithmetic function $mu_{m}(n)$ by$$mu_{m}(n) = ho^{r} quad (ho = e^{2pi i/m}),$$ where $m$ is a naturalnumber. We further define the function $L(s, mu_{m})$ by the Dirichlet series$$L(s, mu_{m}) = sum_{n=1}^{infty} rac{mu_{m}(n)}{n^{s}} = prod_{p}Bigl( 1-rac{ho}{p^{s}} Bigr)^{-1} quad (Re s > 1), $$ and will showthat $L(s, mu_{m})$, $(m geq 3)$, has an infinitely many valued analyticcontinuation into the half plane $Re s > 1/2$.
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机译：令$ n = p_ {1} p_ {2} cdots p_ {r} $是不一定是不同的$ r $质数的乘积。然后我们定义一个算术函数$ mu_ {m}（n）$ by $$ mu_ {m}（n）= rho ^ {r} quad（ rho = e ^ {2 pi i / m} ），$$，其中$ m $是自然数。我们进一步通过Dirichlet系列定义函数$ L（s， mu_ {m}）$$$ L（s， mu_ {m}）= sum_ {n = 1} ^ { infty} frac { mu_ {m}（n）} {n ^ {s}} = prod_ {p} Bigl（1- frac { rho} {p ^ {s}} Bigr）^ {-1} quad（ Re s> 1），$$并且将显示$ L（s， mu_ {m}）$，$（m geq 3）$具有到半平面$ Re s> 1的无限多值的解析连续性/ 2 $。
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