(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
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