Today I tried to compute $\zeta$(e) but no luck.Here's my approach:- $$\zeta(e)=\sum_{n=1}^\infty 1/n^e$$= $$\sum_{n=1}^\infty 1/(2n)^e$$+$$\sum_{n=0}^\infty 1/(2n+1)^e$$ After that I have no idea what to do.If there exists a rational constant then what is it? and if not what is the proof?
Here I am not trying to find an approximation or a series representation.Some might say that I should use Taylor series but I don't think so that it will help. Any insights?