N. Watt

activity

20152019

most citedDecoupling for perturbed cones and mean square of

∣ ζ (\frac{1}{2} + i t) ∣

1 citations · 1 across the 2 of their papers we have counts for

collaborators

4 papers

math.NT2019

On eigenfunctions of the kernel $\frac{1}{2} + ⌊ \frac{1}{x y} ⌋ - \frac{1}{x y}$

Nigel Watt

The integral kernel $K (x, y) := \frac{1}{2} + ⌊ \frac{1}{x y} ⌋ - \frac{1}{x y}$ ( $0 < x, y \leq 1$ ) has connections with the Riemann zeta-function and a (recently observed) c…

math.NT2018

On eigenvalues of the kernel $\frac{1}{2} + ⌊ \frac{1}{x y} ⌋ - \frac{1}{x y}$ ( $0 < x, y \leq 1$ )

N. Watt

We show that the kernel $K (x, y) = \frac{1}{2} + ⌊ \frac{1}{x y} ⌋ - \frac{1}{x y}$ ( $0 < x, y \leq 1$ ) has infinitely many positive eigenvalues and infinitely many negative eigenvalue…

math.NT2018

Mertens Sums requiring Fewer Values of the Möbius function

M. N. Huxley, N. Watt

We discuss certain identities involving $μ (n)$ and $M (x) = \sum_{n \leq x} μ (n)$ , the functions of Möbius and Mertens. These identities allow calculation of $M (N^{d})$ , for $d=2,3,4,\ldo…

math.NT2015★ 1 cited

Decoupling for perturbed cones and mean square of $∣ ζ (\frac{1}{2} + i t) ∣$

Jean Bourgain, Nigel Watt

An improved estimate is obtained for the mean square of the modulus of the zeta function on the critical line. It is based on the decoupling techniques in harmonic analysis develop…

On eigenfunctions of the kernel 21​+⌊xy1​⌋−xy1​

On eigenvalues of the kernel 21​+⌊xy1​⌋−xy1​ (0<x,y≤1)

Mertens Sums requiring Fewer Values of the Möbius function

Decoupling for perturbed cones and mean square of ∣ζ(21​+it)∣

On eigenfunctions of the kernel $\frac{1}{2} + ⌊ \frac{1}{x y} ⌋ - \frac{1}{x y}$

On eigenvalues of the kernel $\frac{1}{2} + ⌊ \frac{1}{x y} ⌋ - \frac{1}{x y}$ ( $0 < x, y \leq 1$ )

Decoupling for perturbed cones and mean square of $∣ ζ (\frac{1}{2} + i t) ∣$