Explicit Mertens' Theorems for Number Fields
Stephan Ramon Garcia, Ethan Simpson Lee
TL;DR
This paper derives uniform, effective versions of Mertens' theorems for number fields assuming the Generalized Riemann Hypothesis, extending classical results to a broader algebraic setting.
Contribution
It provides the first explicit, effective formulations of Mertens' theorems for number fields under the GRH assumption.
Findings
Uniform, effective bounds for prime ideals in number fields
Extension of classical Mertens' theorems to algebraic number fields
Conditional results based on the Generalized Riemann Hypothesis
Abstract
Assuming the Generalized Riemann Hypothesis we obtain uniform, effective number-field analogues of Mertens' theorems.
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Taxonomy
TopicsAnalytic Number Theory Research · History and Theory of Mathematics