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Zhang-Zagier heights of perturbed polynomials

Christophe Doche (2001)

Journal de théorie des nombres de Bordeaux

In a previous article we studied the spectrum of the Zhang-Zagier height [2]. 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 find a limit point less than 1 . 289735 i.e. better than the previous one, namely 1 . 2916674 . After some definitions we detail the principle of the algorithm, the results it gives and the construction that leads to this new limit point.

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