Campana points, Height zeta functions, and log Manin's conjecture

TL;DR

This paper discusses a recent formulation of the log Manin's conjecture for klt Campana points and explores an approach to prove it using height zeta functions, connecting arithmetic geometry and analytic number theory.

Contribution

It introduces a new formulation of the log Manin's conjecture for klt Campana points and proposes an approach via height zeta functions.

Findings

Formulation of log Manin's conjecture for klt Campana points

Proposed approach using height zeta functions

Discussion of analytic number theory techniques

Abstract

This is a report of the author's talk at RIMS workshop 2020 Problems and Prospects in Analytic Number Theory held online on Zoom. We discuss a recent formulation of log Manin's conjecture for klt Campana points and an approach to this conjecture using the height zeta function method.