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COMPUTING HILBERT-KUNZ FUNCTIONS OF 1DIMENSIONAL GRADED RINGS

COMPUTING HILBERT-KUNZ FUNCTIONS OF 1DIMENSIONAL GRADED RINGS,MARTIN KREUZER

COMPUTING HILBERT-KUNZ FUNCTIONS OF 1DIMENSIONAL GRADED RINGS   (Citations: 1)
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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+'(i) where c(R) is the multiplicity of R and ' is a periodic function. Here we study explicit computer algebra algorithms for computing such Hilbert-Kunz functions: the period length and the values of ', as well as a concrete number N ‚ 0 such that the description above holds for i ‚ N.
Published in 2007.
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