洪有情Yu-Ching Hung林永來Yung-Lai Lin2019-09-052003-07-012019-09-052002http://etds.lib.ntnu.edu.tw/cgi-bin/gs32/gsweb.cgi?o=dstdcdr&s=id=%22N2002000010%22.&%22.id.&http://rportal.lib.ntnu.edu.tw:80/handle/20.500.12235/101863缺In this article, by making use of Gr¨obner basis, we determine the Hilbert-Kunz function of binomial hypersurfaces of the form f := Xa1 1 · · ·Xar r Y b1 1 · · · Y bs s + Y c1 1 · · · Y cs s Zd1 1 · · ·Zdt t which is HKR(n) = p(r+s+t−1)n + r+s+t−2 Xk=0 fk(n)pkn for n 0, where is a rational number and fk(n) is an eventually periodic function of n for each k. Moreover, we also determine the leading coecient . iHilbert-Kunz