Abstract
We compute explicitly the normal zeta functions of the Heisenberg groups H(R), where R is a compact discrete valuation ring of characteristic zero. These zeta functions occur as Euler factors of normal zeta functions of Heisenberg groups of the form H(O K ), where O K is the ring of integers of an arbitrary number field K, at the rational primes which are non-split in K. We show that these local zeta functions satisfy functional equations upon inversion of the prime.
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Schein was supported by grant 2264/2010 from the Germany-Israel Foundation for Scientific Research and Development and a grant from the Pollack Family Foundation. We acknowledge support by the DFG Sonderforschungsbereich 701 “Spectral Structures and Topological Methods in Mathematics” at Bielefeld University.
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Schein, M.M., Voll, C. Normal zeta functions of the Heisenberg groups over number rings II — the non-split case. Isr. J. Math. 211, 171–195 (2016). https://doi.org/10.1007/s11856-015-1271-8
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DOI: https://doi.org/10.1007/s11856-015-1271-8