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 .
i

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