57 citations · 242 across the 23 of their papers we have counts for
4 papers · 1 filter
Inverse questions for the large sieve
Ben J. Green, Adam J. Harper
Suppose that an infinite set occupies at most residue classes modulo , for every sufficiently large prime . The squares, or more generally the integer…
Additive decompositions of sets with restricted prime factors
Christian Elsholtz, Adam J. Harper
We investigate sumset decompositions of quite general sets with restricted prime factors. We manage to handle certain sets, such as the smooth numbers, even though they have little…
Sharp conditional bounds for moments of the Riemann zeta function
Adam J. Harper
We prove, assuming the Riemann Hypothesis, that \int_{T}^{2T} |ζ(1/2+it)|^{2k} dt \ll_{k} T log^{k^{2}} T for any fixed k \geq 0 and all large T. This is sharp up to the value of t…
A note on the maximum of the Riemann zeta function, and log-correlated random variables
Adam J. Harper
In recent work, Fyodorov and Keating conjectured the maximum size of in a typical interval of length O(1) on the critical line. They did this by modelling the zeta fu…