J. Lichtman

activity

20152026

most citedThe Erdos conjecture for primitive sets

12 citations · 67 across the 28 of their papers we have counts for

collaborators

Showing 2020Show all

4 papers · 1 filter

math.NT2020★ 2 cited

On the critical exponent for $k$ -primitive sets

Tsz Ho Chan, Jared Duker Lichtman, Carl Pomerance

A set of positive integers is primitive (or 1-primitive) if no member divides another. Erdős proved in 1935 that the weighted sum $\sum 1/ (n lo g n)$ for $n$ ranging over a primitiv…

math.NT2020★ 3 cited

Averages of the Möbius function on shifted primes

Jared Duker Lichtman

It is a folklore conjecture that the Möbius function exhibits cancellation on shifted primes; that is, $\sum_{p \leq X} μ (p + h) = o (π (X))$ as $X \to \infty$ for any fixed shift $h > 0$ …

math.NT2020

A generalization of primitive sets and a conjecture of Erdős

Tsz Ho Chan, Jared Duker Lichtman, Carl Pomerance

A set of integers greater than 1 is primitive if no element divides another. Erdős proved in 1935 that the sum of $1/ (n lo g n)$ for $n$ running over a primitive set $A$ is univers…

math.NT2020★ 1 cited

Mertens' prime product formula, dissected

Jared Duker Lichtman

In 1874, Mertens famously proved an asymptotic formula for the product $p / (p - 1)$ over all primes $p$ up to $x$ . On the other hand, one may expand Mertens' prime product into series…

On the critical exponent for k-primitive sets

Averages of the Möbius function on shifted primes

A generalization of primitive sets and a conjecture of Erdős

Mertens' prime product formula, dissected

On the critical exponent for $k$ -primitive sets