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The Ehrhart function for symbols and a generalization of Euler's constant.





Ehrhart from EulerMacLaurin.


Simple and non-simple polytopes.

Simple

Non-simple


Some references for the exact Euler-MacLaurin formula in higher dimensions.


Regular polytopes.


Regular and nonregular polytopes.


The KhovanskiiPukhlikov formula, 1.


The KhovanskiiPukhlikov formula, 2, moving the facets.


The KhovanskiiPukhlikov formula,3, the Todd operator.


The KhovanskiiPukhlikov formula.


Symbols.


Polyhomogeneous symbols.

n


The order of a symbol.


The Ehrhart formula.



The constant C .



Independence of regularization.



The polar decomposition theorem.




The construction in general.


Polar decomposition.



Using unweighted sums.


The Euler-MacLaurin formula with remainder.




A very rough outline of the proof.


The limiting form of the remainder.











Relation to Euler's gamma.



Relation of C(s) to the zeta function.