Thomas Morrill

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20182020

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3 papers · 1 filter

math.NT2018

An elementary bound on Siegel zeroes

Thomas Morrill, Tim Trudgian

We consider Dirichlet $L$ -functions $L (s, χ)$ where $χ$ is a real, non-principal character modulo $q$ . Using Pintz's refinement of Page's theorem, we prove that for $q \geq 3$ the f…

math.NT2018

Robin's inequality for 20-free integers

Thomas Morrill, David Platt

In 1984, Robin showed that the Riemann Hypothesis for $ζ$ is equivalent to demonstrating $σ (n) < e^{γ} n lo g lo g n$ for all $n > 5040$ . Robin's inequality has since been proven for…

math.HO2018

Difference Tones in "Non-Pythagorean" Scales Based on Logarithms

Thomas Morrill

In order to explore tonality outside of the `Pythagorean' paradigm of integer ratios, Robert Schneider introduced a musical scale based on the logarithm function. We seek to refine…