Normal zeta functions of the Heisenberg groups over number rings I - the unramified case

Abstract

Let $K$ be a number field with ring of integers ${\mathcal{O}}_K$. We compute explicitly the local factors of the normal zeta functions of the Heisenberg groups $H({\mathcal{O}}_K)$ that are indexed by rational primes which are unramified in $K$. We show that these local zeta functions satisfy functional equations upon the inversion of the prime.

30 pages; to appear in J. London Math. Soc; typos removed

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