Let P-n(y(1), ... y(n)) := Pi(1 <= i <= j <= n )(1 - y(i)/y(j)) and P-n := sup((y1, ..., yn) )P(n )(y(1), ..., y(n)) where the supremum is taken over the n-pies (y(1), ..., y(n)) of real numbers satisfying 0 < vertical bar y(1)< vertical bar y(2)vertical bar < ... < vertical bar y(n)&VERBAR(;). We prove that P-n <= 2(left perpendicularn/2right perpendicular) 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.

Generalization of a Pohst's inequality / F. Battistoni, G. Molteni. - In: JOURNAL OF NUMBER THEORY. - ISSN 0022-314X. - 228(2021 Nov), pp. 73-86. [10.1016/j.jnt.2021.04.014]

Generalization of a Pohst's inequality

F. Battistoni
;
G. Molteni
2021

Abstract

Let P-n(y(1), ... y(n)) := Pi(1 <= i <= j <= n )(1 - y(i)/y(j)) and P-n := sup((y1, ..., yn) )P(n )(y(1), ..., y(n)) where the supremum is taken over the n-pies (y(1), ..., y(n)) of real numbers satisfying 0 < vertical bar y(1)< vertical bar y(2)vertical bar < ... < vertical bar y(n)&VERBAR(;). We prove that P-n <= 2(left perpendicularn/2right perpendicular) 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.
Explicit bounds; Totally real fields
Settore MAT/05 - Analisi Matematica
Settore MAT/02 - Algebra
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/870289
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