Toric varieties, lattice points and Dedekind sums
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 begin with a lattice N isomorphic to Z. The dual lattice M of N is given by Hom(N,Z); it is also isomorphic to Z. (The alphabet may appear to be going backwards; but this notation is standard in the literature.) We write the pairing of v ∈ N and w ∈M as 〈v, w〉. A cone in N is a subset of the real vector space NR = N ⊗R generated by nonnegative R-linear combinations of a set of vectors {v1, ....
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The area A inside a simple closed curve C can be estimated graphically by drawing a square lattice of sides 1/M. The number of lattice points inside C is approximately AM. If C has continuous non-zero radius of curvature, then the number of lattice points is accurate to order of magnitude at most M for any a> §. We show that if the radius of curvature of C is continuously differentiate, then th...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 1993
ISSN: 0025-5831,1432-1807
DOI: 10.1007/bf01444874