3 papers
math.NT2024
On several irrationality problems for Ahmes series
Vjekoslav Kovač, Terence Tao
Using basic tools of mathematical analysis and elementary probability theory we address several problems on the irrationality of series of distinct unit fractions, .…
math.NT2023
The convergence of an alternating series of Erdős, assuming the Hardy--Littlewood prime tuples conjecture
Terence Tao
It is an open question of Erdős as to whether the alternating series is (conditionally) convergent, where denotes the $n^{\mathrm{th}…
math.NT2023
A lower bound on the mean value of the Erdős-Hooley Delta function
Kevin Ford, Dimitris Koukoulopoulos, Terence Tao
We give an improved lower bound for the average of the Erdős-Hooley function , namely for all $x\geqslant…