Summary
For each complex number its transcendence type is defined as a non-negative real number, which supplies a measure of its approximability by algebraic numbers. The distribution of complex numbers according to their transcendence types is studied and the existence of complex numbers with a given transcendence type is proved.
Sunto
Per ogni numero complesso è definito il suo tipo di trascendenza come un numero reale non negativo che fornisce una misura della sua approssimabilità mediante numeri algebrici. Si studia la distribuzione dei numeri complessi in relazione al loro tipo di transcendenza e viene dimostrata l'esistenza di numeri complessi aventi tipo di trascendenza assegnato.
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References
F.Amoroso,On the transcendence type of the classical numbers, Boll. U.M.I. (in print).
P. Cijsouw,Transcendence measures, Akademisch Proefschrift, Amsterdam, 1972.
H. Federer,Geometric Measures Theory, Springer-Verlag, Berlin - Heidelberg - New York, 1969.
W. Hurewicz -H. Wallman,Dimension Theory, Princeton University Press, Princeton, N. J., 1941.
P. Philippon,Sur les mesures d'indépendance algébrique, in: Séminaire de Théorie des Nombres, Paris, 1983–84 (C. Goldstein, Ed.), pp. 219–233, Boston — Basel — Stuttgart, Birkhäuser Verlag (Progress in Math.), 1985.
C. A. Rogers,Hausdorff measures, Cambridge University Press, Cambridge (1970).
M. Waldschmidt,Nombres Transcendants, Springer-Verlag (Lecture Notes in Math., no. 402), Berlin - Heidelberg- New York, 1974.
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Amoroso, F. On the distribution of complex numbers according to their transcendence types. Annali di Matematica pura ed applicata 151, 359–368 (1988). https://doi.org/10.1007/BF01762804
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DOI: https://doi.org/10.1007/BF01762804