38 citations · 115 across the 39 of their papers we have counts for
6 papers · 2 filters
The average of the first invariant factor for reductions of CM elliptic curves mod
Tristan Freiberg, Paul Pollack
Let be a fixed elliptic curve. For each prime of good reduction, write , where…
Bounded gaps between primes with a given primitive root, II
Roger C. Baker, Paul Pollack
Let be a natural number, and let be a set containing at least primes. We show that one can find infinitely many strings of consecutive primes each…
Besicovitch, Bisection, and the normality of
Paul Pollack, Joseph Vandehey
We revisit Besicovitch's 1935 paper in which he introduced several techniques that have become essential elements of modern combinatorial methods of normality proofs. Despite his p…
Bounded gaps between primes with a given primitive root
Paul Pollack
Fix an integer that is not a perfect square. In 1927, Artin conjectured that there are infinitely many primes for which is a primitive root. Forty years later, Hool…
Arithmetic functions at consecutive shifted primes
Paul Pollack, Lola Thompson
For each of the functions and every natural number , we show that there are infinitely many solutions to the inequalities $f(p_n-1) < f(p_{n+1}-1) < \dots…
Bounded gaps between primes in number fields and function fields
Abel Castillo, Chris Hall, Robert J. Lemke Oliver +2
The Hardy--Littlewood prime -tuples conjecture has long been thought to be completely unapproachable with current methods. While this sadly remains true, startling breakthroughs…