# Concave Dirichlet series.

There is given function $$f(x)=\sum_{n=1}^{\infty} \frac{a_{n}}{n^{x}}$$ That function converges for non-negative real numbers and is concave on interval $$<0,1>$$ Also $$f(0)=f(1)$$ I am looking for properties of sequence $$(a_{n})_{n>0}$$ Could someone write me at least a tip? Thanks in advance. Here is similar question: Fourier coefficient of convex function

• Well, since $\;f(0)\;$ exists then $\;\sum a_n\;$ converges and thus $\;\lim a_n=0\;$ ...This is trivial, though. – DonAntonio Dec 24 '18 at 20:01