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(Deninger's) Lefschetz trace formula

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[1] C. Deninger, "Motivic L-functions and regularized determinants", Proc. Symp. Pure Math. 55 1 (1994) 707-743.

[2] C. Deninger, "Some ideas on dynamical systems and the Riemann zeta function" (preprint from proceedings of the 1997 ESI conference on the Riemann zeta function)

[3] C. Deninger, "Some analogies between number theory and dynamical systems on foliated spaces", Documenta Mathematica, Extra Volume ICM I (1998) 163-186. [PS format]

[4] C. Deninger, "A note on arithmetic topology and dynamical systems"

[5] C. Deninger, "On the nature of the 'explicit formulas' in analytic number theory - a simple example"

[6] C. Deninger, "Number theory and dynamical systems on foliated spaces"

[7] A. Deitmar and C. Deninger, "A dynamical Lefschetz trace formula for algebraic Anosov diffeomorphisms"

In the papers [2] and [3], Deninger considers dynamical systems (flows) on foliated manifolds. Much like the Selberg-Weil coincidence, he has identified a similarity between

  • the trace formulae for such flows (relating periodic orbits and spectra) and
     
  • certain explicit formulae for the Dedekind zeta functions associated with number fields (these generalise the Riemann zeta function which is a special case when the number field in question is ℝ). This relates to Deninger's earlier arguments [1] in favour of a possible cohomological interpretation of the Riemann zeta function.

C. Deninger's home page

trace formulae, explicit formulae and number theory page