The limit as p -> infinity of the Hilbert-Kunz multiplicity of sum(x_i^(d_i))

Details The limit as p -> infinity of the Hilbert-Kunz multiplicity of sum(x_i^(d_i)) The limit as p -> infinity of the Hilbert-Kunz multiplicity of sum(x_i^(d_i))

2010-07-12

arxiv.org/abs/1007.2004v1

Mathematics

Commutative Algebra

6 pages

Scientific paper

Let p be a prime. The Hilbert-Kunz multiplicity, mu, of the element
sum(x_i^(d_i)) of (Z/p)[x_1,..., x_s] depends on p in a complicated way. We
calculate the limit of mu as p -> infinity. In particular when each d_i is 2 we
show that the limit is 1 + the coefficient of z^(s-1) in the power series
expansion of sec z + tan z.

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