CPL - Chalmers Publication Library

# An elementary proof of the Briancon-Skoda theorem

Jacob Sznajdman (Institutionen för matematiska vetenskaper)
Ann. fac. sci. Toulouse (0240-2963). Vol. Ser. 6, Vol. 19 (2010), 3-4, p. 11.

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.