Lectures on height zeta functions: At the confluence of algebraic geometry, algebraic number theory, and analysis

Antoine Chambert-Loir (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

These is a survey on the theory of height zeta functions, written on the occasion of a French-Japanese winter school, held in Miura (Kanagawa, Japan) in Jan. 2008. It does not presuppose much knowledge in algebraic geometry. The last chapter of the survey explains recent results obtained in collaboration with Yuri Tschinkel concerning asymptotics of volumes of height balls in analytic geometry over local fields, or in adelic spaces.

Domaines: Théorie des nombres [math.NT]; Géométrie algébrique [math.AG]

Antoine Chambert-Loir. Lectures on height zeta functions: At the confluence of algebraic geometry, algebraic number theory, and analysis. MSJ Memoirs, 2010, 21, pp.17-49. ⟨hal-00343210⟩