12 citations · 67 across the 28 of their papers we have counts for
28 papers
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…
Primes in arithmetic progressions to large moduli, and Goldbach beyond the square-root barrier
Jared Duker Lichtman
We show the primes have level of distribution using triply well-factorable weights. This gives the highest level of distribution for primes in any setting, im…
Higher Mertens constants for almost primes II
Jonathan Bayless, Paul Kinlaw, Jared Duker Lichtman
For , let denote the reciprocal sum up to of numbers with prime factors, counted with multiplicity. In prior work, the authors obtained estimates for $R_k(x…
On Erdős sums of almost primes
Ofir Gorodetsky, Jared Duker Lichtman, Mo Dick Wong
In 1935, Erdős proved that the sums , over integers with exactly prime factors, are bounded by an absolute constant, and in 1993 Zhang proved that $…
Primes in arithmetic progressions to large moduli, and shifted primes without large prime factors
Jared Duker Lichtman
We prove the infinitude of shifted primes without prime factors above . This refines from Baker and Harman in 1998. Consequently, we obtain an improv…
A proof of the Erdős primitive set conjecture
Jared Duker Lichtman
A set of integers greater than 1 is primitive if no member in the set divides another. Erdős proved in 1935 that the series is uniformly bounded…
On the Hardy-Littlewood-Chowla conjecture on average
Jared Duker Lichtman, Joni Teräväinen
There has been recent interest in a hybrid form of the celebrated conjectures of Hardy-Littlewood and of Chowla. We prove that for any and distinct integers $h_2,\ldot…
Translated sums of primitive sets
Jared Duker Lichtman
The Erdős primitive set conjecture states that the sum , ranging over any primitive set of positive integers, is maximized by the set of…
A modification of the linear sieve, and the count of twin primes
Jared Duker Lichtman
We introduce a modification of the linear sieve whose weights satisfy strong factorization properties, and consequently equidistribute primes up to size in arithmetic progressi…
Higher Mertens constants for almost primes
Jonathan Bayless, Paul Kinlaw, Jared Duker Lichtman
For , a -almost prime is a positive integer with exactly prime factors, counted with multiplicity. In this article we give elementary proofs of precise asymptotics fo…
On the critical exponent for -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 for ranging over a primitiv…
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, as for any fixed shift …
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…
Mertens' prime product formula, dissected
Jared Duker Lichtman
In 1874, Mertens famously proved an asymptotic formula for the product over all primes up to . On the other hand, one may expand Mertens' prime product into series…
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…