If f(s) = 1 + 1/2^s + 1/3^s + 1/4^s + ...

If s belongs to the set of all complex numbers and It has trivial zeros at the negative even integers (i.e. at s = −2, −4, −6, ...).

Prove that all non-trivial zeros lie on the verticle line: 1/2 + it, where t is a real number and i is the imaginary unit.

Question

If f(s) = 1 + 1/2^s + 1/3^s + 1/4^s + ...

If s belongs to the set of all complex numbers and It has trivial zeros at the negative even integers (i.e. at s = −2, −4, −6, ...).

Prove that all non-trivial zeros lie on the verticle line: 1/2 + it, where t is a real number and i is the imaginary unit.

anonymous · Answer

Haha, If only it were as simply solved as asking in a forum.