Dave Platt

activity

20122020

most citedAccurate estimation of sums over zeros of the Riemann zeta-function

20 citations · 52 across the 14 of their papers we have counts for

collaborators

Showing 2018Show all

3 papers · 1 filter

math.NT2018★ 3 cited

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.NT2018

Fujii's development on Chebyshev's conjecture

Dave Platt, Tim Trudgian

Chebyshev presented a conjecture after observing the apparent bias towards primes congruent to $3 (mod 4)$ . His conjecture is equivalent to a version of the Generalised Riemann Hypo…