3 papers
math.NT2025
Pair Correlation Conjecture for the zeros of the Riemann zeta-function II: The Alternative Hypothesis
Daniel A. Goldston, Junghun Lee, Jordan Schettler +1
In an earlier paper, we proved that Montgomery's Pair Correlation Conjecture (PCC) for zeros of the Riemann zeta-function can be used to prove without the assumption of the Riemann…
math.NT2021
Small Gaps Between Three Almost Primes and Almost Prime Powers
Daniel A. Goldston, Apoorva Panidapu, Jordan Schettler
A positive integer is called an -number if it is the product of distinct primes. We prove that there are infinitely many triples of -numbers within a gap size of …
math.NT2020
Small gaps between almost primes, the parity problem, and some conjectures of Erdős on consecutive integers II
Daniel A. Goldston, Sidney W. Graham, Apoorva Panidapu +3
This paper is intended as a sequel to a paper arXiv:0803.2636 written by four of the coauthors here. In the paper, they proved a stronger form of the Erdős-Mirksy conjecture which…