Omega Estimate for the Lattice Point Discrepancy of a Body of Revolution Using The Resonance Method

2025/06/27 by Karak, Nilmoni
#11K38 #11P21 #52C07 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2506.22590

Abstract

Using a recent method developed by Mahatab, we obtain an improved Ω-bound for the error term arising in lattice counting problem of bodies of revolution in \mathbb R³ around a coordinate axis and having smooth boundary with bounded nonzero curvature. This strengthens an earlier result by Kühleitner and Nowak.

Citations

• Omega Results for The Divisor and Circle Problems Using The Resonance Method
• Extreme values of the Riemann zeta function on the 1-line
• Lattice points in rotated convex domains
• On lattice points in large convex bodies
• Omega results for the divisor and circle problems

Related

• Lattice points in bodies of revolution II
• Omega results for the divisor and circle problems
• The lattice discrepancy of certain three-dimensional bodies
• Ω-results for the hyperbolic lattice point problem
• Reprint: On lattice points in n -dimensional star bodies (1946)