Thomas Morrill

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20182020

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math.NT2019

Inequalities for the $d$ th Residual Crank Moments of Overpartitions

Ali H. Al-Saedi, Thomas Morrill, Holly Swisher

Two analogues of the crank function are defined for overpartitions -- the first residual crank and the second residual crank. This suggests an exploration of crank functions define…

math.NT2019

Sign changes in the prime number theorem

Thomas Morrill, Dave Platt, Tim Trudgian

Let $V (T)$ denote the number of sign changes in $ψ (x) - x$ for $x \in [1, T]$ . We show that $lim inf_{T \to \infty} V (T) / lo g T \geq γ_{1} / π + 1.867 \cdot 1 0^{- 30}$ , where $γ_{…

Inequalities for the dth Residual Crank Moments of Overpartitions

Sign changes in the prime number theorem

Inequalities for the $d$ th Residual Crank Moments of Overpartitions