29 citations · 82 across the 14 of their papers we have counts for
15 papers · 1 filter
Lower bounds for low moments of character sums, I: Short sums with general multiplicative weights
Adam J. Harper
We establish sharp lower bounds for the Dirichlet character moments , where is a large prime, $1 \leq x \l…
Distribution of random multiplicative functions in short intervals, with proper normalization
Adam J. Harper, Kannan Soundararajan, Max Wenqiang Xu
We determine the limiting distribution of partial sums of a Steinhaus random multiplicative function over short intervals , where $y \rightar…
A note on character sums over short moving intervals
Adam J. Harper
We investigate the sums , where is a fixed non-principal Dirichlet character modulo a prime , and is uniformly r…
Almost sure large fluctuations of random multiplicative functions
Adam J. Harper
We prove that if is a Steinhaus or Rademacher random multiplicative function, there almost surely exist arbitrarily large values of for which $|\sum_{n \leq x} f(n)| \ge…
On the partition function of the Riemann zeta function, and the Fyodorov--Hiary--Keating conjecture
Adam J. Harper
We investigate the ``partition function'' integrals for the critical exponent 2, and the local maxima $\max_{|h| \leq 1/2} |ζ(1/2 + it +…
The Riemann zeta function in short intervals [after Najnudel, and Arguin, Belius, Bourgade, Radziwiłł, and Soundararajan]
Adam J. Harper
This is the text to accompany my Bourbaki seminar from 30th March 2019, on the maximum size of the Riemann zeta function in "almost all" intervals of length 1 on the critical line.…