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Trivedi","submitted_at":"2017-07-19T07:29:35Z","abstract_excerpt":"For a toric pair $(X, D)$, where $X$ is a projective toric variety of dimension $d-1\\geq 1$ and $D$ is a very ample $T$-Cartier divisor, we show that the Hilbert-Kunz density function $HKd(X, D)(\\lambda)$ is the $d-1$ dimensional volume of ${\\overline {\\mathcal P}}_D \\cap \\{z= \\lambda\\}$, where ${\\overline {\\mathcal P}}_D\\subset {\\mathbb R}^d$ is a compact $d$-dimensional set (which is a finite union of convex polytopes).\n  We also show that, for $k\\geq 1$, the function\n  $HKd(X, kD)$ can be replaced by another compactly supported continuous function $\\varphi_{kD}$ which is `linear in $k$'. 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