Leung, Naichung Conan; Ma, Ziming Nikolas Lattice points counting via Einstein metrics. (English) Zbl 1267.53047 J. Differ. Geom. 92, No. 1, 55-69 (2012). The authors obtain a growth estimate for the number of lattice points inside any \(\mathbb Q\)-Gorenstein cone. The proof uses the result of Futaki-Ono-Wang on Sasaki-Einstein metric for the toric Sasakian manifold associated to the cone, a Yau inequality, and the Kawasaki-Riemann-Roch formula for orbifolds. Reviewer: A. Arvanitoyeorgos (Patras) MSC: 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 52C07 Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry) 16E65 Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) 13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) Keywords:Gorenstein cone; Sasakian manifold; Kawasaki-Riemann-Roch formula; Einstein metric PDF BibTeX XML Cite \textit{N. C. Leung} and \textit{Z. N. Ma}, J. Differ. Geom. 92, No. 1, 55--69 (2012; Zbl 1267.53047) Full Text: DOI arXiv Euclid