大次随机多项式的不可约性

IF 5.4 3区材料科学 Q2 CHEMISTRY, PHYSICAL

ACS Applied Energy Materials Pub Date : 2018-10-31 DOI:10.4310/ACTA.2019.v223.n2.a1

E. Breuillard, P. P. Varj'u

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引用次数: 27

摘要

我们考虑具有独立同分布系数的随机多项式，具有固定律。假设Dedekind-zeta函数的Riemann假设，我们证明了这样的多项式是不可约的，并且它们的Galois群包含随着次数变为无穷大而具有高概率的交替群。这解决了Odlyzko和Poonen关于Dedekind-zeta函数RH的条件猜想。

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Irreducibility of random polynomials of large degree

We consider random polynomials with independent identically distributed coefficients with a fixed law. Assuming the Riemann hypothesis for Dedekind zeta functions, we prove that such polynomials are irreducible and their Galois groups contain the alternating group with high probability as the degree goes to infinity. This settles a conjecture of Odlyzko and Poonen conditionally on RH for Dedekind zeta functions.

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来源期刊

ACS Applied Energy Materials Materials Science-Materials Chemistry

CiteScore

10.30

自引率

6.20%

发文量

1368

期刊介绍： ACS Applied Energy Materials is an interdisciplinary journal publishing original research covering all aspects of materials, engineering, chemistry, physics and biology relevant to energy conversion and storage. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrate knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important energy applications.