An elementary proof of the Briancon-Skoda theorem

Journal article, 2010

We give an elementary proof of the Briancon-Skoda theorem. The theorem gives a criterion for when a function \phi belongs to an ideal I of the ring of germs of analytic functions at 0 \in ℂ^n; more precisely, the ideal membership is obtained if a function associated with \phi and I is locally square integrable. If I can be generated by m elements, it follows in particular that the integral closure of I^min(m,n) is contained in I.