What the study found
The study found an improved Omega-bound for the error term in a lattice counting problem for bodies of revolution in three-dimensional space. In this setting, a body of revolution is a shape formed by rotating a curve around an axis.
Why the authors say this matters
The authors say this strengthens an earlier result by K"uhleitner and Nowak. The study suggests the newer method gives a better lower-bound estimate for the size of the discrepancy term.
What the researchers tested
The researchers applied a recent method developed by Mahatab. They studied lattice counting for bodies of revolution around a coordinate axis with smooth boundary and bounded nonzero curvature.
What worked and what didn't
The approach produced an improved Omega-bound for the error term. The abstract does not describe any failed cases, comparisons beyond the earlier result, or numerical details.
What to keep in mind
The summary only states that the result applies to bodies of revolution in R^3 with smooth boundary and bounded nonzero curvature. No further limitations or caveats are described in the abstract.
Key points
- An improved Omega-bound was obtained for the lattice point discrepancy error term.
- The problem concerns bodies of revolution in three-dimensional space.
- The shapes considered have smooth boundaries and bounded nonzero curvature.
- The result strengthens an earlier result by K"uhleitner and Nowak.
- The work uses a recent method developed by Mahatab.
Disclosure
- Research title:
- Improved Omega bound for lattice point discrepancy in bodies of revolution
- Authors:
- Nilmoni Karak
- Institutions:
- Indian Institute of Technology Kharagpur
- Publication date:
- 2026-04-27
- OpenAlex record:
- View
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