Variations on theorems of Mertens
Nobushige Kurokawa, Hidekazu Tanaka
TL;DR
This paper explores variations of Mertens' theorems within the framework of the Density Hypothesis and examines Serre's estimate related to the Lang-Weil estimate, advancing understanding in number theory and algebraic geometry.
Contribution
It introduces new variations of Mertens' theorems as special cases of the Density Hypothesis and analyzes Serre's estimate in the context of Lang-Weil estimates.
Findings
New variations of Mertens' theorems established
Connections between Density Hypothesis and classical theorems shown
Insights into Serre's estimate related to Lang-Weil provided
Abstract
We present variations on theorems of Mertens as special cases of Density Hypothesis. Moreover, we study a Serre's estimate concerning Lang-Weil estimate.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Functional Equations Stability Results · Advanced Banach Space Theory