ISSN:
1573-8876
Keywords:
multiplicative function
;
additive divisor problem
;
Riemann zeta function
;
Euler function
;
primitive characters
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract For multiplicative functions ƒ(n), let the following conditions be satisfied: ƒ(n)≥0 ƒ(p r)≤A r,A〉0, and for anyε〉0 there exist constants $$A_\varepsilon$$ ,α〉0 such that $$f(n) \leqslant A_\varepsilon n^\varepsilon$$ and Σ p≤x ƒ(p) lnp≥αx. For such functions, the following relation is proved: $$\sum\limits_{n \leqslant x} {f(n)} \tau (n - 1) = C(f)\sum\limits_{n \leqslant x} {f(n)lnx(1 + 0(1))}$$ . Hereτ(n) is the number of divisors ofn andC(ƒ) is a constant.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02314849
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