Dedekind-Rademacher sums and lattice points in triangles and tetrahedra
نویسندگان
چکیده
منابع مشابه
Lattice Points, Dedekind Sums, and Ehrhart Polynomials of Lattice Polyhedra
Let σ be a simplex of RN with vertices in the integral lattice ZN . The number of lattice points of mσ (= {mα : α ∈ σ}) is a polynomial function L(σ,m) of m ≥ 0. In this paper we present: (i) a formula for the coefficients of the polynomial L(σ, t) in terms of the elementary symmetric functions; (ii) a hyperbolic cotangent expression for the generating functions of the sequence L(σ,m), m ≥ 0; (...
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We give explicit, polynomial–time computable formulas for the number of integer points in any two– dimensional rational polygon. A rational polygon is one whose vertices have rational coordinates. We find that the basic building blocks of our formulas are Dedekind–Rademacher sums, which are polynomial–time computable finite Fourier series. As a by–product we rederive a reciprocity law for these...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1981
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-39-1-59-75