N. Watt

activity

20132024

most citedMean square of zeta function, circle problem and divisor problem revisited

33 citations · 44 across the 10 of their papers we have counts for

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Showing 2018Show all

3 papers · 1 filter

math.NT2018

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

Nigel Watt

We study the eigenvalues $λ_{1}, λ_{2}, λ_{3}, \dots$ (ordered by modulus) of the integral kernel $K (x, y) := \frac{1}{2} + ⌊ \frac{1}{x y} ⌋ - \frac{1}{x y}$ ( $0 < x, y \leq 1$ ). Th…

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…

On eigenvalues of the kernel 21​+⌊xy1​⌋−xy1​, II

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

Mertens Sums requiring Fewer Values of the Möbius function

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

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