Let [Formula presented] and Pn:=sup(y1,…,yn)Pn(y1,…,yn) where the supremum is taken over the n-ples (y1,…,yn) of real numbers satisfying 0<|y1|<|y2|<⋯<|yn|. We prove that Pn≤2⌊n/2⌋ for every n, i.e., we extend to all n the bound that Pohst proved for n≤11. As a consequence, the bound for the absolute discriminant of a totally real field in terms of its regulator is now proved for every degree of the field.
Battistoni, F., Molteni, G., Generalization of a Pohst's inequality, <<JOURNAL OF NUMBER THEORY>>, 2021; 228 (N/A): 73-86. [doi:10.1016/j.jnt.2021.04.014] [https://hdl.handle.net/10807/270246]
Generalization of a Pohst's inequality
Battistoni, Francesco
;
2021
Abstract
Let [Formula presented] and Pn:=sup(y1,…,yn)Pn(y1,…,yn) where the supremum is taken over the n-ples (y1,…,yn) of real numbers satisfying 0<|y1|<|y2|<⋯<|yn|. We prove that Pn≤2⌊n/2⌋ for every n, i.e., we extend to all n the bound that Pohst proved for n≤11. As a consequence, the bound for the absolute discriminant of a totally real field in terms of its regulator is now proved for every degree of the field.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
