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Primitive sets and von Mangoldt chains: Erdős Problem #1196 and beyond
Boris Alexeev, Kevin Barreto, Yanyang Li +5
A set of integers is primitive if no number in the set divides another. We introduce a new method for bounding Erdős sums of primitive sets, suggested from output of GPT-5.4 Pro, b…
The conjecture is true almost always
Jared Duker Lichtman
Let denote the product of distinct prime factors of an integer . The celebrated conjecture asks whether every solution to the equation in trip…
Erdős's integer dilation approximation problem and GCD graphs
Dimitris Koukoulopoulos, Youness Lamzouri, Jared Duker Lichtman
Let be a countable set such that . We prove that, for ev…
Bounds on the exceptional set in the conjecture
Christian Bernert, Tim Browning, Jared Duker Lichtman +1
We study solutions to the equation , where form a triple of coprime natural numbers. The conjecture asserts that, for any , such triples satisfy $\mathrm{…
Density theorems for via Rankin-Selberg -functions
Jared Duker Lichtman, Alexandru Pascadi
We obtain density theorems for cuspidal automorphic representations of over which fail the generalized Ramanujan conjecture at some place. We depart from…
The Bombieri-Pila determinant method
Thomas F. Bloom, Jared Duker Lichtman
We give a concise and accessible introduction to the real-analytic determinant method for counting integral points on algebraic curves, based on the classic 1989 paper of Bombieri…