Abstract
In this paper we study the compatibility of Manin’s conjectures concerning asymptotics of rational points on algebraic varieties with certain natural geometric constructions. More precisely, we consider locally trivial fibrations constructed from torsors under linear algebraic groups. The main problem is to understand the behaviour of the height function as one passes from fiber to fiber - a difficult problem, even though all fibers are isomorphic. We will be mostly interested in fibrations induced from torsors under split tori. Asymptotic properties follow from analytic properties of height zeta functions. Under reasonable assumptions on the analytic behaviour of the height zeta function for the base we establish analytic properties of the height zeta function of the total space.
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Chambert-Loir, A., Tschinke, Y. (2001). Fonctions ZÊta Des Hauteurs Des Espaces Fibrés. In: Peyre, E., Tschinkel, Y. (eds) Rational Points on Algebraic Varieties. Progress in Mathematics, vol 199. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8368-9_4
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DOI: https://doi.org/10.1007/978-3-0348-8368-9_4
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