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 -