Proves Erdős-Kac type central limit theorems for the number of ramified primes in random G-extensions of number fields when G is abelian, including first examples of dependent local ramification events.
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The paper proves two Tauberian theorems, one with the power-saving error term x^{α-δ/(κ+1)} (log x)^{m-1}, and builds counterexamples showing the error terms are near-optimal, refuting a stronger claim in the literature.
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Erd\H{o}s-Kac theorems for discriminants of number fields
Proves Erdős-Kac type central limit theorems for the number of ramified primes in random G-extensions of number fields when G is abelian, including first examples of dependent local ramification events.
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A guide to Tauberian theorems for arithmetic applications
The paper proves two Tauberian theorems, one with the power-saving error term x^{α-δ/(κ+1)} (log x)^{m-1}, and builds counterexamples showing the error terms are near-optimal, refuting a stronger claim in the literature.