What is the Definition of a Trace and Can it Prove the Riemann Hypothesis?

[zetafunction]

the idea is this, for the mathematician what is exactly the definition of a Trace ??

for example let us suppose that i find a trace operator for Riemann Zeros, then would it mean that i have solved Riemann Hypothesis ??

In the paper: http://www.math.ohio-state.edu/lectures/connes/zeta2.pdf

they say 'if the Trace xxx is correct then RH is proved'

but in order to prove a Trace is correct you only would need to test it with several functions, wouldn't you

 

[0xDEADBEEF]

[...]
but in order to prove a Trace is correct you only would need to test it with several functions, wouldn't you

Why do you say that? This is like saying all odd numbers except 1 are prime:
3 is prime ,5 is prime, 7 is prime -- it's proven!