57 citations · 242 across the 23 of their papers we have counts for
4 papers · 1 filter
Orderings of weakly correlated random variables, and prime number races with many contestants
Adam J. Harper, Youness Lamzouri
We investigate the race between prime numbers in many residue classes modulo , assuming the standard conjectures GRH and LI. Among our results we exhibit, for the first time, pr…
Maxima of a randomized Riemann zeta function, and branching random walks
Louis-Pierre Arguin, David Belius, Adam J. Harper
A recent conjecture of Fyodorov--Hiary--Keating states that the maximum of the absolute value of the Riemann zeta function on a typical bounded interval of the critical line is $\e…
A note on Helson's conjecture on moments of random multiplicative functions
Adam J. Harper, Ashkan Nikeghbali, Maksym Radziwiłł
We give lower bounds for the small moments of the sum of a random multiplicative function, which improve on some results of Bondarenko and Seip and constitute further progress towa…
Mean values of multiplicative functions over function fields
Andrew Granville, Adam J. Harper, Kannan Soundararajan
We discuss the mean values of multiplicative functions over function fields. In particular, we adapt the authors' new proof of Halasz's theorem on mean values to this simpler setti…