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math.CO2005★ 10 cited
Ehrhart-Macdonald reciprocity extended
Matthias Beck, Richard Ehrenborg
For a convex polytope P with rational vertices, we count the number of integer points in integral dilates of P and its interior. The Ehrhart-Macdonald reciprocity law gives an inti…
math.NT2005
Determinations of Analogues of Gauss Sums and Other Trigonometric Sums
Matthias Beck, Bruce C. Berndt, O-Yeat Chan +1
Explicit determinations of several classes of trigonometric sums are given. These sums can be viewed as analogues or generalizations of Gauss sums. In a previous paper, two of the…