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A prime geodesic theorem for SL4

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Abstract

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.

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  1. Mathematics Department, University of Tuebingen, Auf der Morgenstelle 10, Tuebingen, 72076, Germany

    Anton Deitmar & Mark Pavey

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  1. Anton Deitmar
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  2. Mark Pavey
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Correspondence to Anton Deitmar.

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Deitmar, A., Pavey, M. A prime geodesic theorem for SL4 . Ann Glob Anal Geom 33, 161–205 (2008). https://doi.org/10.1007/s10455-007-9078-4

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