Trace formula in noncommutative geometry and the Riemann hypothesis

In summary, the conversation involves discussing a paper titled "Formule de trace en géométrie non-commutative et hypothèse de Riemann" and its availability. The original link to purchase the paper is broken and leads to an infinite redirect loop. The journal homepage and table of contents are also not accessible. However, the paper can be found at a different link. There is also a discussion about the content of the paper and its translation to English.
  • #1
crowlogic
6
0
Does anyone know where to find this paper?

Formule de trace en géométrie non-commutative et hypothèse de Riemann = Trace formula in noncommutative geometry and the Riemann hypothesis

http://cat.inist.fr/?aModele=afficheN&cpsidt=2561461

The purchase link is broken there.. it gets stuck in an infinite page redirect loop. I found the journal homepage at http://www.elsevier.com/wps/find/journaldescription.cws_home/600301/description#description and the link to the table of contents points to http://www.elseviermathematics.com/ but this page is completely blank! What gives?

I think the paper seems interesting because he contructs a Frobenius-Perron operator from a classical map whose eigenvalues are the riemann zeros.
 
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  • #3
perhaps policy forums do not let you post here a copyrighted material ( this paper is supposed to be payed) , anyway i do not understand why author of paper 'ignores' the contribution from the sum over primes in the paper or how could he construct a Hamiltonian from this Trace
 
  • #4
Then I guess I'll do a translation and post that at some point
 
  • #5
Last edited by a moderator:

What is the trace formula in noncommutative geometry?

The trace formula in noncommutative geometry is a mathematical formula that relates the trace of an operator on a noncommutative space to the sum of the eigenvalues of that operator. It is a fundamental tool in studying the geometry and topology of noncommutative spaces.

Why is the trace formula important in noncommutative geometry?

The trace formula is important because it allows us to study the geometry and topology of noncommutative spaces, which are abstract mathematical objects that do not have a traditional notion of distance or coordinates. The trace formula provides a way for us to understand and analyze these spaces using concepts from more familiar geometry.

What is the relation between the trace formula and the Riemann hypothesis?

The trace formula is closely related to the Riemann hypothesis, which is one of the most famous unsolved problems in mathematics. The Riemann hypothesis states that all nontrivial zeros of the Riemann zeta function lie on the critical line with real part equal to 1/2. The trace formula has been used to make progress towards proving the Riemann hypothesis and has provided insights into the connections between number theory and noncommutative geometry.

How does the trace formula in noncommutative geometry differ from the trace formula in traditional geometry?

The trace formula in noncommutative geometry is different from the trace formula in traditional geometry because it applies to noncommutative spaces, whereas the traditional trace formula applies to spaces that have a well-defined notion of distance and coordinates. Noncommutative spaces are more abstract and require specialized tools, such as the trace formula, for their study.

What are some applications of the trace formula in noncommutative geometry?

The trace formula in noncommutative geometry has many applications, including in number theory, quantum mechanics, and string theory. It has been used to study the Riemann hypothesis, to understand the behavior of quantum systems, and to explore connections between geometry and physics. It also has potential applications in cryptography and coding theory.

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