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

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In summary, the definition of a trace for a mathematician is a way to measure the sum of the elements in a linear transformation. However, finding a trace operator for Riemann Zeros does not necessarily mean that the Riemann Hypothesis has been solved. In the paper provided, it is stated that if the trace is proven to be correct, then the Riemann Hypothesis is also proven. However, it is not as simple as testing the trace with several functions, as shown by the example where all odd numbers except 1 are proven to be prime based on a few tests.
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zetafunction
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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
 
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zetafunction said:
[...]
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!
 

What is exactly a Trace?

A trace is a set of data points that represent the progression of a variable over time.

What is the purpose of tracing?

The purpose of tracing is to understand the behavior of a system or variable over time in order to identify patterns, anomalies, or potential issues.

What types of data can be traced?

Any type of data that can be measured over time can be traced, such as temperature, pressure, or computer system performance metrics.

What are some common techniques used in tracing?

Some common techniques used in tracing include event-based tracing, statistical tracing, and distributed tracing.

How is tracing different from monitoring?

Tracing is a type of monitoring that focuses on understanding the behavior of a system or variable over time, while monitoring can also include real-time alerts and notifications for specific events or conditions.

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