7 papers
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 for running over a primitive set is univers…
Almost primes and the Banks-Martin conjecture
Jared Duker Lichtman
It has been known since Erdos that the sum of over numbers with exactly prime factors (with repetition) is bounded as varies. We prove that as tends t…
A Refined Conjecture for the Variance of Gaussian Primes Across Sectors
Ryan C. Chen, Yujin H. Kim, Jared D. Lichtman +6
We derive a refined conjecture for the variance of Gaussian primes across sectors, with a power saving error term, by applying the L-functions Ratios Conjecture. We observe a bifur…
Primes in prime number races
Jared Duker Lichtman, Greg Martin, Carl Pomerance
Rubinstein and Sarnak have shown, conditional on the Riemann hypothesis (RH) and the linear independence hypothesis (LI) on the non-real zeros of , that the set of real numbe…
The Erdos conjecture for primitive sets
Jared Duker Lichtman, Carl Pomerance
A subset of the integers larger than 1 is if no member divides another. Erdos proved in 1935 that the sum of for running over a primitive set is u…
Spectral Statistics of Non-Hermitian Random Matrix Ensembles
Ryan C. Chen, Yujin H. Kim, Jared D. Lichtman +3
Recently Burkhardt et. al. introduced the -checkerboard random matrix ensembles, which have a split limiting behavior of the eigenvalues (in the limit all but of the eigenva…