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Let $I_n(J) = (I^n \\colon J^\\infty)$ be the $n^{th}$ symbolic power of $I$ \\wrt \\ $J$. It is easy to see that the function $f^I_J(n) = e_0(I_n(J)/I^n)$ is of quasi-polynomial type, say of period $g$ and degree $c$. For $n \\gg 0$ say \\[ f^I_J(n) = a_c(n)n^c + a_{c-1}(n)n^{c-1} + \\text{lower terms},\n  \\] where for $i = 0, \\ldots, c$, $a_i \\colon \\mathbb{N} \\rt \\mathbb{Z}$ are periodic functions of period $g$ and $a_c \\neq 0$.\n  In an earlier paper we (together with Herzog and Verma) proved that $\\dim I_n(J)/I^n$ is constant","authors_text":"Tony J. 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