On the number of integer points in a multidimensional domain
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Alexander S. Rybakov
Abstract
We provide a new upper estimate for the modulus of the difference |Λ ∩ 𝓢| − voln(𝓢)/det Λ, where 𝓢 ⊂ ℝn is a set of volume voln(𝓢) and Λ ⊂ ℝn is a complete lattice with determinant det Λ. This result has an important practical application, for example, in estimating the number of integer solutions of an arbitrary system of linear and nonlinear inequalities.
Originally published in Diskretnaya Matematika (2017) 29,№4, 106–120 (in Russian).
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Estimate of the maximal cycle length in the graph of polynomial transformation of Galois–Eisenstein ring
- Durfee squares in compositions
- On fault detection tests of contact break for contact circuits
- On the number of integer points in a multidimensional domain
- On Stone’s renewal theorem for arithmetic distributions
- Local limit theorems for one class of distributions in probabilistic combinatorics
Artikel in diesem Heft
- Frontmatter
- Estimate of the maximal cycle length in the graph of polynomial transformation of Galois–Eisenstein ring
- Durfee squares in compositions
- On fault detection tests of contact break for contact circuits
- On the number of integer points in a multidimensional domain
- On Stone’s renewal theorem for arithmetic distributions
- Local limit theorems for one class of distributions in probabilistic combinatorics
