In the region 0 < Re(s) < 1 we know that
$$ \zeta(s) = 1/(1-2^{1-s}) \sum_1^\infty (-1)^{n+1}/n^s\,. $$
This is a multiplication of two complex numbers.
Question 1: Am I right to suppose that in case of zeros of $$\zeta(s), 0 < Re(s) < 1 $$ either the summation term, or the term before the summation has to be zero?
Question 2: If that is true, then am I right to suppose that it is the summation term that will always be zero?
Thanks.