We deduce asymptotic formulas for the alternating sums $sum_{nle x} (-1)^{n-1} f(n)$and $sum_{nle x} (-1)^{n-1} rac1{f(n)}$, where f is one of the following classical multiplicative arithmetic functions: Euler's totient function, the Dedekind function, the sum-of-divisors function, the divisor function, the gcd-sum function. We also consider analogs of these functions, which are associated to unitary and exponential divisors, and other special functions. Some of our results improve the error terms obtained by Bordellès and Cloitre. We formulate certain open problems.
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机译：我们推论出交替总和$ sum_ {n le x}（-1）^ {n-1} f（n）$和$ sum_ {n le x}（-1）^ {n- 1} frac1 {f（n）} $，其中f是以下经典乘法运算函数之一：欧拉的totient函数，Dedekind函数，除数和函数，除数函数，gcd-sum函数。我们还考虑了与单数和指数除数以及其他特殊功能相关的这些功能的类似物。我们的某些结果改善了Bordellès和Cloitre得出的误差项。我们提出了一些未解决的问题。
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