57 citations · 242 across the 23 of their papers we have counts for
4 papers · 1 filter
Extreme biases in prime number races with many contestants
Kevin Ford, Adam J. Harper, Youness Lamzouri
We continue to investigate the race between prime numbers in many residue classes modulo , assuming the standard conjectures GRH and LI. We show that provided $n/\log q \rightar…
A more intuitive proof of a sharp version of Halász's theorem
Andrew Granville, Adam J Harper, K. Soundararajan
We prove a sharp version of Halász's theorem on sums of multiplicative functions with . Our proof avoids the "average of averages" and "inte…
A new proof of Halász's Theorem, and its consequences
Andrew Granville, Adam J Harper, K. Soundararajan
Halász's Theorem gives an upper bound for the mean value of a multiplicative function . The bound is sharp for general such , and, in particular, it implies that a multiplica…
Moments of random multiplicative functions, I: Low moments, better than squareroot cancellation, and critical multiplicative chaos
Adam J. Harper
We determine the order of magnitude of , where is a Steinhaus or Rademacher random multiplicative function, and . In…