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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This guide details hypotheses and proofs for two Tauberian theorems (with and without remainder) and supplies counterexamples showing that stronger conclusions require stronger hypotheses.
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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
This guide details hypotheses and proofs for two Tauberian theorems (with and without remainder) and supplies counterexamples showing that stronger conclusions require stronger hypotheses.