English

Igusa integrals and volume asymptotics in analytic and adelic geometry

Number Theory 2009-12-24 v2 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.0909.1568,
  title  = {Igusa integrals and volume asymptotics in analytic and adelic geometry},
  author = {Antoine Chambert-Loir and Yuri Tschinkel},
  journal= {arXiv preprint arXiv:0909.1568},
  year   = {2009}
}

Comments

75 pages

R2 v1 2026-06-21T13:44:06.214Z