论文标题
无条件的明确默滕斯定理数字字段和dedekind Zeta残留界限
Unconditional Explicit Mertens' Theorems for Number Fields and Dedekind Zeta Residue Bounds
论文作者
论文摘要
我们获得了三个Mertens定理的无条件，有效的数字类似物，所有这些定理都具有显式常数，对$ x \ geq 2 $有效。我们的错误项是根据数字字段的程度和判别性明确界定的。为此，我们为相应的Dedekind Zeta函数的残基提供无条件的界限，并在$ s = 1 $中提供无条件的界限。
We obtain unconditional, effective number-field analogues of the three Mertens' theorems, all with explicit constants and valid for $x\geq 2$. 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 $s=1$.
