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

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SUMMARY

The discussion centers on the definition of a Trace in relation to the Riemann Hypothesis (RH). It highlights the assertion from a paper by Alain Connes that proving the correctness of a Trace operator for Riemann Zeros could lead to a proof of RH. Participants debate the validity of testing a Trace's correctness through examples, comparing it to a flawed argument about prime numbers. The conversation underscores the complexity of mathematical proofs and the necessity of rigorous validation beyond mere examples.

PREREQUISITES
  • Understanding of mathematical concepts related to the Riemann Hypothesis
  • Familiarity with Trace operators in functional analysis
  • Knowledge of Riemann Zeros and their significance in number theory
  • Basic comprehension of mathematical proof techniques
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  • Study Alain Connes' paper on the Trace and its implications for the Riemann Hypothesis
  • Research the properties and applications of Trace operators in mathematics
  • Explore the concept of Riemann Zeros and their role in analytic number theory
  • Learn about rigorous proof techniques in mathematics to understand validation processes
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Mathematicians, researchers in number theory, and students interested in advanced mathematical concepts related to the Riemann Hypothesis and Trace operators.

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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!
 

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