Average number of local minima for three-dimensional integral lattices

DOI10.1090/S1061-0022-2012-01208-2zbMath1261.11048OpenAlexW2012171366MaRDI QIDQ2892184

A. A. Illarionov

Publication date: 18 June 2012

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1061-0022-2012-01208-2

zbMATH Keywords

latticelocal minimummultidimensional continued fractionEuclid's algorithm

Mathematics Subject Classification ID

Lattices and convex bodies (number-theoretic aspects) (11H06) Continued fractions and generalizations (11J70) Minima of forms (11H50)

Related Items (2)

The statistical properties of 3D Klein polyhedra ⋮ On the statistical properties of Klein polyhedra in three-dimensional lattices

Cites Work

• Statistik der Teilnenner der zu den echten Brüchen gehörigen regelmäßigen Kettenbrüche
• The lower bound for the number of local minima of integral lattices
• Estimate for the number of relative minima of arbitrary-rank incomplete integer lattices
• An introduction to the geometry of numbers.
• Minimal bases of three-dimensional complete lattices
• On a theorem of Heilbronn
• The solution of Arnold's problem on the weak asymptotics of Frobenius numbers with three arguments
• Minimal bases in complete 3-lattices
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