Secondary Term of Asymptotic Distribution of S₃times A Extensions over mathbb{Q}
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We combine a sieve method together with good uniformity estimates to prove a secondary term for the asymptotic estimate of $S_3\times A$ extensions over $\mathbb{Q}$ when $A$ is an odd abelian group with minimal prime divisor greater than $5$. At the same time, we prove the existence of a power saving error when $A$ is any odd abelian group.
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Forward citations
Cited by 3 Pith papers
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Statistics of the Genus Number of $S_3 \times C_q$ and $D_4$-fields
Asymptotic statistics, averages, and higher moments of genus numbers are established for S3×Cq-fields (q prime ≠3), D4-fields, and pure quartic fields, with a heuristic conjecture on zero-density families.
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Statistics of the Genus Number of $S_3 \times C_q$ and $D_4$-fields
Establishes statistics, averages, and moments of genus numbers for S3×Cq, D4, and pure quartic fields, plus a conjecture on zero-density families.
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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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