Annals of Global Analysis and Geometry

, Volume 33, Issue 2, pp 161–205 | Cite as

A prime geodesic theorem for SL4

  • Anton DeitmarEmail author
  • Mark Pavey
Original Paper


A prime geodesic theorem is derived for rank-one geodesics in quotients of SL4. This has applications in class number asymptotics for quartic fields. For these applications it is necessary to prove a more general statement than in the literature: several regularity conditions have to be abandoned. As a consequence, the analytical difficulties multiply. The final result is obtained by a sandwiching argument from infinitely many independent asymptotics.


Prime geodesic theorem Trace formula Ruelle zeta function 


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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of TuebingenTuebingenGermany

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