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• #### Exponential Weighted Sums related to the Divisor and Circle Problems ﻿

(Master thesis, 2018)
The classical results of the Dirichlet Divisor Problem and Gauss' Circle Problem are examined, with required information on the Riemann Zeta function presented. In particular, the results derived from the weighted sums of ...
• #### Extreme values of the Riemann zeta function and its argument ﻿

(Journal article; Peer reviewed, 2018)
We combine our version of the resonance method with certain convolution formulas for ζ(s) and logζ(s) . This leads to a new Ω result for |ζ(1/2+it)| : The maximum of |ζ(1/2+it)| on the interval 1≤t≤T is at ...
• #### Gal-type GCD sums beyond the critical line ﻿

(Journal article; Peer reviewed, 2016)
• #### GCD sums and complete sets of square-free numbers ﻿

(Journal article; Peer reviewed, 2015)
• #### Large greatest common divisor sums and extreme values of the Riemann zeta function ﻿

(Journal article; Peer reviewed, 2017)
• #### Linear space properties of H^p spaces of Dirichlet series ﻿

(Journal article; Peer reviewed, 2019)
We study H p spaces of Dirichlet series, called H p , for the range 0 < p < ∞. We begin by showing that two natural ways to define H p coincide. We then proceed to study some linear space properties of H p . More specifically, ...
• #### Note on the resonance method for the Riemann zeta function ﻿

(Journal article; Peer reviewed, 2018)
We improve Montgomery’s Ω-results for |ζ(σ + it)| in the strip 1/2 σ 1 and give in particular lower bounds for the maximum of |ζ(σ+it)| on √ T ≤ t ≤ T that are uniform in σ. We give similar lower bounds for the maximum of ...
• #### Pseudomoments of the Riemann zeta function ﻿

(Journal article; Peer reviewed, 2018)
The 2kth pseudomoments of the Riemann zeta function ζ ( s ) are, following Conrey and Gamburd, the 2 k th integral moments of the partial sums of ζ ( s ) on the critical line. For fixed k > 1 / 2 , these moments are known ...