Wirsing translation
E. Wirsing, "Das asymptotische verhalten von summen über multiplikative funktionen. II." Acta Mathematica Academiae Scientiarum Hungaricae Tomus 18 (3-4), 1978, pp. 411-467.
English Translation by: Google Translator
In I we have the asymptotic behavior of the sum \ sum_ (n \ leq x) \ lambda (n) for nonnegative multiplicative functions \ lambda essentially under the condition
(1.1) \ frac (p \ leq x) \ lambda (p) \ log (p) \ tilde \ tau x (p prime)
- Determine
N (1.2) \ frac (\ leq x) \ lambda (s) \ tilde \ frac (e ^ (-ct)) (\ Gamma (\ tau)) \ frac (x) (\ log x) \ prod_ (p \ leq x) \ left (1 + \ frac (\ lambda (p)) (p) + \ frac (\ lambda (p ^ (2))) (p ^ (2)) + \ cdots \ right)
(c is the Euler-) constant. Special rates are the same type Delange [3]. The same result
(1.2) is here under the much weaker assumption
(1.3) \ frac (p \ leq x) \ lambda (p) \ frac (\ log p) (p) \ tilde \ tau \ log x
However, with the additional. Call \ lambda (p) = O (1) and only for tau \> are shown 0 (Theorem 1.1). The terms of \ lambda (p ^ (v)) (v \ geq2) are thieves than I, but we want them in the introduction . neglect The same result for complex-Tunktionen \ lambda, we get only if \ lambda by | \ lambda | nich significantly different, namely, if
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