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Unconditional explicit Mertens’ theorems for number fields and Dedekind zeta residue bounds
The Ramanujan Journal ( IF 0.7 ) Pub Date : 2021-05-14 , DOI: 10.1007/s11139-021-00435-6
Stephan Ramon Garcia , Ethan Simpson Lee

We obtain unconditional, effective number-field analogues of the three Mertens’ theorems, all with explicit constants and valid for \(x\ge 2\). Our error terms are explicitly bounded in terms of the degree and discriminant of the number field. To this end, we provide unconditional bounds, with explicit constants, for the residue of the corresponding Dedekind zeta function at \(s=1\).



中文翻译:

数域和Dedekind zeta残差界的无条件显式Mertens定理

我们获得了三个Mertens定理的无条件有效数字域类似物,它们都具有显式常数,并且对\(x \ ge 2 \)有效。我们的错误术语明确地以数字字段的程度和判别为界。为此,我们为\(s = 1 \)处对应的Dedekind zeta函数的残差提供了带有显式常数的无条件范围。

更新日期:2021-05-15
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