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A quantitative Khintchine-Groshev theorem is a theorem for obtaining the asymptotic formula for the function counting integer solutions satisfying inequalities provided by the Khintchine-Groshev theorem. Recently, M. Alam, A. Ghosh, and S. Yu found a new proof for the quantitative Khintchine-Groshev theorem, which further includes the cases adding some congruence conditions.
In this talk, I will introduce its generalization to S-arithmetic spaces and explain why we need a new type of an S-arithmetic generalization for this application, instead of a generalization established by D. Kleinbock and G. Tomanov, for instance.