Computing Hilbert–kunz Functions of 1-dimensional Graded Rings
نویسنده
چکیده
According to a theorem of Monsky, the Hilbert–Kunz function of a 1-dimensional standard graded algebra R over a finite field K has, for i 0, the shape HKR(i) = c(R) · p i + φ(i), where c(R) is the multiplicity of R and φ is a periodic function. Here we study explicit computer algebra algorithms for computing such Hilbert–Kunz functions: the period length and the values of φ, as well as a concrete number N ≥ 0 such that the description above holds for i ≥ N .
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