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arXiv 2007.103132020-07math.NT

Unconditional Explicit Mertens' Theorems for Number Fields and Dedekind Zeta Residue Bounds

Stephan Ramon Garcia, Ethan Simpson Lee

备注：: 19 pages
DOI：: 10.1007/s11139-021-00435-6

英文摘要：

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 $s=1$.

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