The sphere packing problem in dimension 24
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In this article, it was shown that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing.Abstract:
Building on Viazovska's recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing. In particular, we find an optimal auxiliary function for the linear programming bounds, which is an analogue of Viazovska's function for the eight-dimensional case.read more
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References
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Handbook of Mathematical Functions with Formulas
TL;DR: The Handbook of Mathematical Functions with Formulas (HOFF-formulas) as mentioned in this paper is the most widely used handbook for mathematical functions with formulas, which includes the following:
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Tata Lectures on Theta I
TL;DR: In this paper, theta functions in one variable and motivation: motivation and theta function in several variables are compared. But the results are limited to one variable, and motivation is not considered.
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Sphere packings I
TL;DR: A program to prove the Kepler conjecture on sphere packings is described and it is shown that every Delaunay star that satisfies a certain regularity condition satisfies the conjecture.
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Spherical codes and designs
TL;DR: In this paper, the authors provided an overview of spherical codes and designs, and derived bounds for the cardinality of spherical A-codes in terms of the Gegenbauer coefficients of polynomials compatible with A.
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The Selberg trace formula for PSL (2, IR)
TL;DR: The selberg trace formula (version A) as mentioned in this paper is a trace formula for the Poincare series and the spectral decomposition of L2(? \H,?).