Browsing by Author "Deitmar, Anton"

Now showing 1 - 3 of 3

Building lattices and zeta functions
(2020-04-01)
Deitmar, Anton
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Kang, Ming-Hsuan
;
McCallum, Rupert
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應用數學系
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Department of Applied Mathematics
We give a Lefschetz formula for tree lattices and apply it to geometric zeta functions. We further generalize Bass's approach to Ihara zeta functions to the higher-dimensional case of a building.
Tree-Lattice Zeta Functions and Class Numbers
(2018-01-01)
Deitmar, Anton
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Kang, Ming-Hsuan
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應用數學系
;
Department of Applied Mathematics
We extend the theory of Ihara zeta functions to noncompact arithmetic quotients of Bruhat-Tits trees. This new zeta function turns out to be a rational function despite the infinite-dimensional setting. In general, it has zeros and poles in contrast to the compact case. The determinant formulas of Bass and Ihara hold if we define the determinant as the limit of all finite principal minors. From this analysis we derive a prime geodesic theorem, which, applied to special arithmetic groups, yields new asymptotic assertions on class numbers of orders in global fields.
Zeta functions of F-1-buildings
(2016-04)
Deitmar, Anton
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Kang, Ming-Hsuan
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應用數學系
;
Department of Applied Mathematics
The analogue of the Bruhat-Tits building of a p-adic group in F1-geometry is a single apartment. In this setting, the trace formula gives rise to a several variable zeta function analogously to the p-adic case. The analogy carries on to the fact that the restriction to certain lines yield zeta functions which are defined in geometrical terms. Also, the classical formula of Ihara has an analogue in this setting.