Lattice points on a curve via $\ell^2$ decoupling

Publication date: 17 May 2022

Abstract: We prove a generalization of Bombieri-Pila's inequality for lattice points on a curve to proper generalized arithmetic progressions. The proof uses the

e l l^{2}

decoupling inequality for non-degenerate curves in

m a t h b b R^{n}

. We also review the curve-lifting method and use it to establish various estimates of lattice points on a planar curve.

Mathematics Subject Classification ID

Lattice points in specified regions (11P21)

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