For smooth convex bodies of revolution in R^3, the lattice point discrepancy satisfies P_B(t) = Omega_-(t^(1/2)(log t)^(1/3)(log_2 t)^((2/3)(sqrt(2)-1))(log_3 t)^(-1/3)), improving the prior exponent of log_3 t from -2/3 to -1/3.
Kr¨ atzel, Lattice points, Mathematics and its Applications (East European Series), 33, Kluwer Acad
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Omega Estimate for the Lattice Point Discrepancy of a Body of Revolution Using The Resonance Method
For smooth convex bodies of revolution in R^3, the lattice point discrepancy satisfies P_B(t) = Omega_-(t^(1/2)(log t)^(1/3)(log_2 t)^((2/3)(sqrt(2)-1))(log_3 t)^(-1/3)), improving the prior exponent of log_3 t from -2/3 to -1/3.