4 citations · 7 across the 11 of their papers we have counts for
11 papers
Zero-free regions inspired by work of Heath-Brown
Chiara Bellotti, Tim Trudgian, Andrew Yang
We prove a new explicit zero-free region for the Riemann zeta-function, drawing substantially on Heath-Brown's seminal work on Linnik's constant. Using these ideas we are able to p…
Explicit bounds for the Riemann zeta-function on the 1-line
Ghaith A. Hiary, Nicol Leong, Andrew Yang
Explicit estimates for the Riemann zeta-function on the -line are derived using various methods, in particular van der Corput lemmas of high order and a theorem of Borel and Car…
Toward optimal exponent pairs
Timothy S. Trudgian, Andrew Yang
We quantify the set of known exponent pairs and develop a framework to compute the optimal exponent pair for an arbitrary objective function. Applying this methodology,…
On the generalised Dirichlet divisor problem
Chiara Bellotti, Andrew Yang
We improve unconditional estimates on , the remainder term of the generalised divisor function, for large . In particular, we show that $Δ_k(x) \ll x^{1 - 1.889k^{-2/3}}…
An explicit sub-Weyl bound for
Dhir Patel, Andrew Yang
In this article we prove an explicit sub-Weyl bound for the Riemann zeta function on the critical line . In particular, we show that $|ζ(1/2 + it)| \le 66.7\,…
Explicit bounds on in the critical strip and a zero-free region
Andrew Yang
We derive explicit upper bounds for the Riemann zeta-function on the lines for integer . This is used to show that the zeta-function has no…
Explicit zero-free regions for the Riemann zeta-function
Michael J. Mossinghoff, Timothy S. Trudgian, Andrew Yang
We prove that the Riemann zeta-function has no zeros in the region for . In addition, we improve th…
An improved explicit estimate for
Ghaith A. Hiary, Dhir Patel, Andrew Yang
An explicit subconvex bound for the Riemann zeta function on the critical line is proved. Previous subconvex bounds relied on an incorrect version of the Kusmin-L…
Some explicit estimates for the error term in the prime number theorem
Daniel R. Johnston, Andrew Yang
By combining and improving recent techniques and results, we provide explicit estimates for the error terms , and appearing in the prime…
Outdegree conditions forcing short cycles in digraphs
Dan Ismailescu, Joonsoo Lee, Andrew Yang
Given a positive integer , let be the smallest positive constant with the following property: \emph{ Every simple directed graph on vertices all whose outd…
On the number of integral binary -ic forms having bounded Julia invariant
Manjul Bhargava, Andrew Yang
In 1848, Hermite introduced a reduction theory for binary forms of degree which was developed more fully in the seminal 1917 treatise of Julia. This canonical method of reducti…