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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2026 2verdicts
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Develops square-annular dynamics for the T(n)=n+τ(n) graph, establishes transfer identities and bounds on E_k, and gives a connectedness criterion conditional on liminf |A_k(E_k)|=1, plus unconditional R(X) and sum bounds via shifted-square estimates.
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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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Square-Annular Dynamics and Coalescence Frontiers for $n+\tau(n)$
Develops square-annular dynamics for the T(n)=n+τ(n) graph, establishes transfer identities and bounds on E_k, and gives a connectedness criterion conditional on liminf |A_k(E_k)|=1, plus unconditional R(X) and sum bounds via shifted-square estimates.