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mhill
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What is the so called Connes trace and its relation to Riemann Hypothesis proposed by the physicist COnnes ? , or in fact how it would be related to Riemann Hypothesis
Connes Trace and Its Relation to Riemann Hypothesis: An Overview
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In summary, the Connes trace, proposed by physicist Alain Connes, is a concept related to the Riemann Hypothesis and Berry Conjecture, which can be traced back to mathematicians Polya and Hilbert. It has also been studied in the context of the Riemann zeta function and quantum chaos by Eugene Bogomolny and Landau levels and Riemann zeros by German Sierra and Paul K. Townsend. However, the perspective and understanding of this concept may differ between physicists and number theory experts.
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atyy
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Berry Conjecture (I just found out it goes back to Polya and Hilbert!)
http://mathworld.wolfram.com/BerryConjecture.html
Riemann zeta function and quantum chaos
Eugene Bogomolny
http://arxiv.org/abs/0708.4223
Landau levels and Riemann zeros
German Sierra, Paul K. Townsend
http://arxiv.org/abs/0805.4079
Well, or at least that's what they teach in quantum mechanics. I've no idea if a number theory person would see it the same way. Connes is a physicist?
http://mathworld.wolfram.com/BerryConjecture.html
Riemann zeta function and quantum chaos
Eugene Bogomolny
http://arxiv.org/abs/0708.4223
Landau levels and Riemann zeros
German Sierra, Paul K. Townsend
http://arxiv.org/abs/0805.4079
Well, or at least that's what they teach in quantum mechanics. I've no idea if a number theory person would see it the same way. Connes is a physicist?
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1. What is Connes Trace and its relation to Riemann Hypothesis?
Connes Trace is a mathematical concept developed by Alain Connes in the 1970s. It is a functional trace on a certain class of operators called "trace class" operators. The Riemann Hypothesis is a famous unsolved problem in mathematics that deals with the distribution of prime numbers. Connes Trace has been used in attempts to prove the Riemann Hypothesis.
2. How is Connes Trace related to the Riemann zeta function?
The Riemann zeta function is a complex-valued function that is closely related to the distribution of prime numbers. Connes Trace has been used to define a functional equation for the Riemann zeta function, which is a key component in proving the Riemann Hypothesis.
3. What are some applications of Connes Trace and its relation to the Riemann Hypothesis?
Connes Trace and its relation to the Riemann Hypothesis has been applied in various areas of mathematics, including number theory, topology, and operator algebra. It has also been used in attempts to prove other unsolved problems, such as the Generalized Riemann Hypothesis.
4. What progress has been made in using Connes Trace to prove the Riemann Hypothesis?
While Connes Trace has shown promise in approaching the Riemann Hypothesis, it has not yet led to a proof. Some progress has been made in using Connes Trace to prove weaker versions of the Riemann Hypothesis, but the full conjecture remains unsolved.
5. Are there any controversies or criticisms surrounding Connes Trace and its relation to the Riemann Hypothesis?
As with any mathematical approach to a major unsolved problem, there have been debates and criticisms about the validity and effectiveness of using Connes Trace to prove the Riemann Hypothesis. Some argue that it may not be a fruitful approach, while others believe it holds potential for a breakthrough in solving the Riemann Hypothesis.
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