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  • 1
    Electronic Resource
    Electronic Resource
    Problems similar to the additive divisor problem (1996)
    Springer
    Mathematical notes 64 (1996), S. 382-393 
    Details
    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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