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Wild Partitions And Number Theory, David P. Roberts

Mathematics Publications

We introduce the notion of wild partition to describe in combinatorial language an important situation in the theory of p-adic fields. For Q a power of p, we get a sequence of numbers λ_Q,n counting the number of certain wild partitions of n. We give an explicit formula for the corresponding generating function Λ_Q(x) = Σλ_Q,nx^_n and use it to show that λ^1/n _Q,n tends to Q^1/(p-1). We apply this asymptotic result to support a finiteness conjecture about number fields. Our finiteness conjecture …