Develops multiple Dirichlet series methods to count G-extensions for infinitely many new Galois groups G, with unconditional results for concentrated groups and conditional asymptotics including all nilpotency class 2 groups.
Power savings for counting (twisted) abelian extensions of number fields
2 Pith papers cite this work. Polarity classification is still indexing.
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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.
citing papers explorer
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Counting number fields using multiple Dirichlet series
Develops multiple Dirichlet series methods to count G-extensions for infinitely many new Galois groups G, with unconditional results for concentrated groups and conditional asymptotics including all nilpotency class 2 groups.
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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.