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Generalization of a Pohst's inequality
Journal of Number Theory ( IF 0.6 ) Pub Date : 2021-05-31 , DOI: 10.1016/j.jnt.2021.04.014
Francesco Battistoni , Giuseppe Molteni

LetPn(y1,,yn):=1i<jn(1yiyj) andPn:=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 Pn2n/2 for every n, i.e., we extend to all n the bound that Pohst proved for n11. 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.



中文翻译:

Pohst 不等式的推广

n(1,,n)=1一世<jn(1-一世j)n=(1,,n)n(1,,n)其中supremum接管了n(1,,n) 实数满足 0<|1|<|2|<<|n|. 我们证明n2n/2对于每个n,即,我们将Pohst 证明的界限扩展到所有nn11. 因此,现在证明了一个完全实域的绝对判别式在其调节器方面的界限,适用于该域的每一级。

更新日期:2021-05-31
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