Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896846 | Journal of Number Theory | 2018 | 16 Pages |
Abstract
We study an optimal stretching problem for certain convex domain in Rd (dâ¥3) whose boundary has points of vanishing Gaussian curvature. We prove that the optimal domain which contains the most positive (or least nonnegative) lattice points is asymptotically balanced. This type of problem has its origin in the “eigenvalue optimization among rectangles” problem in spectral geometry. Our proof relies on two-term bounds for lattice counting for general convex domains in Rd and an explicit estimate of the Fourier transform of the characteristic function associated with the specific domain under consideration.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jingwei Guo, Weiwei Wang,