Igusa integrals and volume asymptotics in analytic and adelic geometry
By Antoine Chambert-Loir, Yuri Tschinkel. 2009
89 citations recorded by the source corpus.
We establish asymptotic formulae for volumes of height balls in analytic varieties over local fields and in adelic points of algebraic varieties over number fields, relating the Mellin transforms of height functions to Igusa integrals and to global geometric invariants of the underlying variety. In the adelic setting, this involves the construction of general Tamagawa measures.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/062b0aae807578e5ec0d2df4a8c57a7794a4984e
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Geometric Manin’s conjecture and rational curves (2017, result): “for some ǫ > 0. Moreover its leading term is given by lim s→a(X,L) Z(X,q,s)(1− q (a X,L)−s r )b(X,L) = Mqnα(X,L)(b(X,L) −1)!. for some positive integer M determined by the number of components. By [CLT10] the following asymptotic statement would be a consequence: N(X,L,q,d) ∼ MqdimXα(X,L) 1− q−a(”