In principle, also real analytic functions, with possibly rational coefficients, make sense. The notion of conformal confinement with zeros of ζ interpreted as mass squared values and conformal weights, makes ζ and L-functions as its generalizations physically unique real analytic functions.
If the conjecture stating that the roots of ζ are algebraic numbers is true, the virtual momenta of fermions could be algebraic integers for virtual fermions and integers for the physical states also for ζ. This makes sense if the notions of Galois group and Galois confinement are sensible notions for ζ.
In this article, the properties of ζ and its symmetric variant ξ and their multi-valued inverses are studied. In particular, the question whether ξ might have no finite critical points is raised.
See the article Some comments of the physical interpretation of Riemann zeta in TGD.
For a summary of earlier postings see Latest progress in TGD.
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