Dave Platt

activity

20122020

most citedChern Character for Global Matrix Factorizations

9 citations · 9 across the 2 of their papers we have counts for

collaborators

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6 papers · 1 filter

math.NT2020

The mean square of the error term in the prime number theorem

Richard P. Brent, David J. Platt, Timothy S. Trudgian

We show that, on the Riemann hypothesis, $lim sup_{X \to \infty} I (X) / X^{2} \leq 0.8603$ , where $I (X) = \int_{X}^{2 X} (ψ (x) - x)^{2} d x .$ This proves (and improves on) a claim by Pintz fro…

math.NT2020

The Riemann hypothesis is true up to $3 \cdot 1 0^{12}$

Dave Platt, Tim Trudgian

We verify numerically, in a rigorous way using interval arithmetic, that the Riemann hypothesis is true up to height $3 \cdot 1 0^{12}$ . That is, all zeroes $β + iγ$ of the Riemann zet…

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_{…

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.NT2018

Improved bounds on Brun's constant

Dave Platt, Tim Trudgian

Brun's constant is $B = \sum_{p \in P_{2}} p^{- 1} + (p + 2)^{- 1}$ , where the summation is over all twin primes. We improve the unconditional bounds on Brun's constant to $1.840503 < B…

math.NT2015

Diophantine quintuples containing triples of the first kind

Dave Platt, Tim Trudgian

We consider Diophantine quintuples ${a, b, c, d, e}$ , sets of distinct positive integers the product of any two elements of which is one less than a perfect square. Triples of th…

The mean square of the error term in the prime number theorem

The Riemann hypothesis is true up to 3⋅1012

Sign changes in the prime number theorem

Robin's inequality for 20-free integers

Improved bounds on Brun's constant

Diophantine quintuples containing triples of the first kind

The Riemann hypothesis is true up to $3 \cdot 1 0^{12}$