A Sharp Upper Estimate of the Number of Integral Points in a 5-Dimensional Tetrahedra
Tài liệu tham khảo
Beukers, 1975, The lattice-points of a n-dimensional tetrahedra, Indag. Math., 37, 365, 10.1016/1385-7258(75)90043-8
Cappell, 1994, Genera of algebraic varieties and counting lattice points, Bull. Amer. Math Soc. (N.S.), 30, 62, 10.1090/S0273-0979-1994-00436-7
Durfee, 1978, The signature of smoothings of complex surface singularities, Math. Ann., 232, 85, 10.1007/BF01420624
Ehrhart, 1967, Sur un problème de géométrie diophantienne linéaire, II, J. Reine Angew. Math., 227, 25
A. Granville, letter to Y.-J. Xu.
G. H. Hardy and J. E. Littlewood, Some problems of diophantine approximation, in Proc. 5th Int. Congress of Mathematics, 1912, pp. 223–229.
Hardy, 1921, The lattice points of a right-angled triangle, Proc. London Math. Soc. (2), 20, 15
Hardy, 1922, The lattice points of a right-angled triangle (second memoir), Hamburg Math. Abh., 1, 212
Kantor, 1993, Une application du Théorème de Riemann–Roch combinatoire au polynôme d'Ehrhart des polytopes entier de Rd, C.R. Acad. Sci. Paris Sér. I, 317, 501
Lehmer, 1940, The lattice points of an n-dimensional tetrahedron, Duke Math. J., 7, 341, 10.1215/S0012-7094-40-00719-0
K.-P. Lin, and, S. S.-T. Yau, Sharp upper estimate of geometric genus in terms of Milnor number and multiplicity with application on coordinate free characterization of 3-dimensional homogeneous singularities, preprint.
K.-P. Lin, and, S. S.-T. Yau, Analysis of sharp polynomial upper estimate of number of positive integral points in a 4-dimensional tetrahedra, J. Reine Angew. Math, to appear.
Merle, 1980, Conditions d'adjonction d'après Du Val, Séminaire sur les singularités des surfaces, Centre de Math. de l'Ecole Polytechnique, 1976–1977
Milnor, 1970, Isolated singularities defined by weighted homogeneous polynomials, Topology, 9, 385, 10.1016/0040-9383(70)90061-3
Mordell, 1951, Lattice points in tetrahedron and generalized Dedekind sums, J. Indian Math. Soc., 15, 41
Pommershim, 1993, Toric variety, lattice points and Dedekind sums, Math. Ann., 295, 1, 10.1007/BF01444874
C. Pomerance, The role of smooth numbers in number theoretic algorithms, pp. 411–422, ICM, Zürich, 1994.
C. Pomerance, Lecture notes on primality testing and factoring: A short course, Kent State University, 1984.
Rosser, 1939, On the first case of Fermat's last theorem, Bull. Amer. Math. Soc., 45, 636, 10.1090/S0002-9904-1939-07058-4
Spencer, 1939, On a Hardy–Littlewood problem of diophantine approximation, Math. Proc. Cambridge Philos. Soc., 35, 527, 10.1017/S0305004100021320
Spencer, 1942, The lattice points of tetrahedra, J. Math. Phys., 21, 189, 10.1002/sapm1942211189
Xu, 1992, Sharp estimate of number of integral points in a tetrahedron, J. Reine Angew. Math., 423, 199
Xu, 1993, Durfee conjecture and coordinate free characterization of homogeneous singularities, J. Differential Geom., 37, 375, 10.4310/jdg/1214453681
Xu, 1996, Sharp estimate of number of integral points in a 4-dimensional tetrahedron, J. Reine Angew. Math., 473, 1
