Igusa integrals and volume asymptotics in analytic and adelic geometry

Details Igusa integrals and volume asymptotics in analytic and adelic geometry Igusa integrals and volume asymptotics in analytic and adelic geometry

2009-09-08

arxiv.org/abs/0909.1568v2

Mathematics

Number Theory

75 pages

Scientific paper

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.

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