J. Lichtman

activity

20242026

most citedPrimitive sets and von Mangoldt chains: ErdÅs Problem #1196 and beyond

1 citations · 1 across the 2 of their papers we have counts for

collaborators

6 papers

math.NT2026

Bounds on the exceptional set in the $ab c$ conjecture

Christian Bernert, Tim Browning, Jared Duker Lichtman +1

We study solutions to the equation $a + b = c$ , where $a, b, c$ form a triple of coprime natural numbers. The $ab c$ conjecture asserts that, for any $I^µ > 0$ , such triples satisfy $\mathrm…

math.NT2026★ 1 cited

Primitive sets and von Mangoldt chains: ErdÅs 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 ErdÅs sums of primitive sets, suggested from output of GPT-5.4 Pro,…

math.NT2025

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…

math.NT2025

The $ab c$ conjecture is true almost always

Jared Duker Lichtman

Let $rad (n)$ denote the product of distinct prime factors of an integer $n \geq 1$ . The celebrated $ab c$ conjecture asks whether every solution to the equation $a + b = c$ in trip…

math.NT2025

ErdÅs's integer dilation approximation problem and GCD graphs

Dimitris Koukoulopoulos, Youness Lamzouri, Jared Duker Lichtman

Let $A \subset R_{⩾ 1}$ be a countable set such that $lim sup_{x \to \infty} \frac{1}{l o g x} \sum_{I^\pm \in A \cap [1, x]} \frac{1}{I ^} \pm > 0$ . We prove that, for…

math.NT2024

A proof of the ErdÅs primitive set conjecture

Jared Duker Lichtman

A set of integers greater than 1 is primitive if no member in the set divides another. ErdÅs proved in 1935 that the series $f (A) = \sum_{a \in A} 1/ (a lo g a)$ is uniformly bounded…

Bounds on the exceptional set in the abc conjecture

Primitive sets and von Mangoldt chains: ErdÅs Problem #1196 and beyond

The Bombieri-Pila determinant method

The abc conjecture is true almost always

ErdÅs's integer dilation approximation problem and GCD graphs

A proof of the ErdÅs primitive set conjecture

Bounds on the exceptional set in the $ab c$ conjecture

Primitive sets and von Mangoldt chains: ErdÅs Problem #1196 and beyond

The $ab c$ conjecture is true almost always

ErdÅs's integer dilation approximation problem and GCD graphs

A proof of the ErdÅs primitive set conjecture