Adam J. Harper

Minor arcs, mean values, and restriction theory for exponential sums over smooth numbers

We investigate exponential sums over those numbers

A Note on Helson’s Conjecture on Moments of Random Multiplicative Functions

\leq x

Orderings of weakly correlated random variables, and prime number races with many contestants

all of whose prime factors are

Sharp conditional bounds for moments of the Riemann zeta function

\leq y

A note on the maximum of the Riemann zeta function, and log-correlated random variables

. We prove fairly good minor arc estimates, valid whenever

Bombieri--Vinogradov and Barban--Davenport--Halberstam type theorems for smooth numbers

\log^{3}x \leq y \leq x^{1/3}

Inverse questions for the large sieve

. Then we prove sharp upper bounds for the

Two new proofs of the Erdös–Kac Theorem, with bound on the rate of convergence, by Stein's method for distributional approximations

p

Additive decompositions of sets with restricted prime factors

-th moment of (possibly weighted) sums, for any real

Moments of random multiplicative functions, II: High moments.

p > 2