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The Ehrhart function for symbols and a generalization of Eulers - - PowerPoint PPT Presentation
The Ehrhart function for symbols and a generalization of Eulers - - PowerPoint PPT Presentation
The Ehrhart function for symbols and a generalization of Eulers constant. Ehrhart from Euler- MacLaurin. Simple and non-simple polytopes. Non-simple Simple Some references for the exact Euler-MacLaurin formula in higher dimensions.
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Ehrhart from Euler- MacLaurin.
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Simple and non-simple polytopes.
Simple Non-simple
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Some references for the exact Euler-MacLaurin formula in higher dimensions.
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Regular polytopes.
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Regular and non- regular polytopes.
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The Khovanskii- Pukhlikov formula, 1.
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The Khovanskii- Pukhlikov formula, 2, moving the facets.
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The Khovanskii- Pukhlikov formula,3, the Todd operator.
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The Khovanskii- Pukhlikov formula.
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Symbols.
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Polyhomogeneous symbols.
n
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The order of a symbol.
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The Ehrhart formula.
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The constant C .
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Independence of regularization.
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The polar decomposition theorem.
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The construction in general.
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Polar decomposition.
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Using unweighted sums.
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The Euler-MacLaurin formula with remainder.
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A very rough outline of the proof.
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The limiting form of the remainder.
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Relation to Euler’s gamma.
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