Zhang-Zagier heights of perturbed polynomials. (English) Zbl 1046.11076

Summary: In a previous article we studied the spectrum of the Zhang-Zagier height [C. Doche, Math. Comput. 70, 419–430 (2001; Zbl 0960.11047)]. The progress we made was based on an algorithm that produces 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.


11R09 Polynomials (irreducibility, etc.)
11G50 Heights


Zbl 0960.11047
Full Text: DOI Numdam EuDML EMIS


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