Derives two-term Weyl formula for Dirichlet eigenvalues on planar annulus with O(μ^{2/3}) remainder (improved to Huxley-type under rational-slope assumption) via Bessel-zero approximations and lattice-point estimates; by-product for disks.
and Watt, N., Mean square of zeta function, circle problem and divisor problem revisited
2 Pith papers cite this work. Polarity classification is still indexing.
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Improved asymptotic for T(x) = ∑_{n≤x} τ([x/n]) τ(n) with error O(x^{17/30+ε}), obtained via new bounds on three-dimensional exponential sums with constant perturbation.
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The Weyl formula for planar annuli
Derives two-term Weyl formula for Dirichlet eigenvalues on planar annulus with O(μ^{2/3}) remainder (improved to Huxley-type under rational-slope assumption) via Bessel-zero approximations and lattice-point estimates; by-product for disks.
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On the Hyperbolic Fractional Sum of the Divisor Function
Improved asymptotic for T(x) = ∑_{n≤x} τ([x/n]) τ(n) with error O(x^{17/30+ε}), obtained via new bounds on three-dimensional exponential sums with constant perturbation.