TY - JOUR
T1 - Normal zeta functions of the Heisenberg groups over number rings II — the non-split case
AU - Schein, Michael M.
AU - Voll, Christopher
N1 - Publisher Copyright:
© 2016, Hebrew University of Jerusalem.
PY - 2016/2/1
Y1 - 2016/2/1
N2 - 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(OK), where OK 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.
AB - 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(OK), where OK 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.
UR - http://www.scopus.com/inward/record.url?scp=84953265423&partnerID=8YFLogxK
U2 - 10.1007/s11856-015-1271-8
DO - 10.1007/s11856-015-1271-8
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AN - SCOPUS:84953265423
SN - 0021-2172
VL - 211
SP - 171
EP - 195
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -