G. Hurst

activity

20092026

most citedAn elementary (number theory) proof of Touchard's congruence

1 citations · 2 across the 3 of their papers we have counts for

collaborators

3 papers

math.NT2026

Practical Computations of the Mertens Function: $M (1 0^{24})$ and $M (1 0^{25})$

Greg Hurst

The Mertens function is defined as $M (x) = \sum_{n \leq x} μ (n)$ , where $μ (n)$ is the Möbius function. This paper describes a practical implementation of the classical $O(x^{2/3+\varep…

math.NT2016★ 1 cited

Computations of the Mertens Function and Improved Bounds on the Mertens Conjecture

Greg Hurst

The Mertens function is defined as $M (x) = \sum_{n \leq x} μ (n)$ , where $μ (n)$ is the Möbius function. The Mertens conjecture states $∣ M (x) / x ∣ < 1$ for $x > 1$ , which was pr…

math.CO2009★ 1 cited

An elementary (number theory) proof of Touchard's congruence

Greg Hurst, Andrew Schultz

Let B_n denote the nth Bell number. We use well-known recursive expressions for B_n to give a generalizing recursion that can be used to prove Touchard's congruence.

Practical Computations of the Mertens Function: M(1024) and M(1025)

Computations of the Mertens Function and Improved Bounds on the Mertens Conjecture

An elementary (number theory) proof of Touchard's congruence

Practical Computations of the Mertens Function: $M (1 0^{24})$ and $M (1 0^{25})$