the Table Maker's Dilemma

Integer points close to a transcendental curve: an algorithmic approach

arXiv:2606.04858v1 Announce Type: cross Abstract: In this article, we propose an algorithmic approach to determine the integer points located near a transcendental curve. This approach is closely related to a celebrated work by Bombieri and Pila and to the so-called Coppersmith's method. We establish the underlying theoretical foundations, prove the algorithms, study their complexity and present practical experiments; we also compare our approach with previously existing ones.