## asymptotic behaviour of functions..

let be f(x) and g(x) 2 arithmetical functions related by:

$$g(x)= \sum_{n=0}^{\infty} f(x/n)h(n)$$

where h(n) is a known function, my question is, if we know that

$$g(x) \sim x^{a}$$ a>0 and real.

What could we say about $$f(x) \sim ?$$ knowing the value of h(n).

i have tried approximating the sum by an integral and we get:

$$g(x)= \int_{0}^{\infty} f(x/u)h(u)du$$
 PhysOrg.com science news on PhysOrg.com >> Galaxies fed by funnels of fuel>> The better to see you with: Scientists build record-setting metamaterial flat lens>> Google eyes emerging markets networks