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Spectral Analysis of the local Commutator Operators
Jean-Francois Burnol
The spectral analysis of the (local) conductor operator H = log(|q|) + log(|p|) was shown in a previous paper to be given by the Explicit Formula. I give here the spectral analysis…
Spectral Analysis of the local Conductor Operator
Jean-Francois Burnol
The conductor operator acts on a function through multiplying it with the logarithm of the norm of the variable both in position and in momentum space and adding the outcomes. It m…
The Explicit Formula in simple terms
Jean-Francois Burnol
This is a semi-expository paper on the easier aspects of the Explicit Formula for the Riemann Zeta Function. The topics reviewed here include: Weil's criterion for the Riemann Hypo…
The Explicit Formula and a Propagator
Jean-Francois Burnol
I give a new derivation of the Explicit Formula for the general number field K, which treats all primes in exactly the same way, whether they are discrete or archimedean, and also…