Zhang-Zagier heights of perturbed polynomials

Abstract In a previous article we studied the spectrum of the ZhangZagier height D The progress we made stood on an algorithm that produced polynomials with a small height In this paper we describe a new algorithm that provides even smaller heights It allows us to nd a limit point less than ie better than the previous one namely After some denitions we detail the principle of the algorithm the results it gives and the construction that leads to this new limit poin

A Survey on the Conjecture of Lehmer and the Conjecture of Schinzel-Zassenhaus

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