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A proof of the Conjecture of Lehmer and of the Conjecture of Schinzel-Zassenhaus

  title={A proof of the Conjecture of Lehmer and of the Conjecture of Schinzel-Zassenhaus},
  author={Jean-Louis Verger-Gaugry},
  journal={arXiv: Number Theory},
The conjecture of Lehmer is proved to be true. The proof mainly relies upon: (i) the properties of the Parry Upper functions f α (z) associated with the dynamical zeta functions ζ α (z) of the Renyi–Parry arithmetical dynamical systems, for α an algebraic integer α of house α greater than 1, (ii) the discovery of lenticuli of poles of ζ α (z) which uniformly equidistribute at the limit on a limit " lenticular " arc of the unit circle, when α tends to 1 + , giving rise to a continuous lenticular… 

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