J. Blackman

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math.NT2023

A Note on the Base- $p$ Expansions of Putative Counterexamples to the $p$ -adic Littlewood Conjecture

John Blackman, Simon Kristensen, Matthew J. Northey

In this paper, we investigate the base- $p$ expansions of putative counterexamples to the $p$ -adic Littlewood conjecture of de Mathan and Teulié. We show that if a counterexample ex…

math.NT2021

Infinite Loops and the $p$ -adic Littlewood Conjecture. Part I: Reformulating the $p$ -adic Littlewood Conjecture in Terms of Infinite Loops

John Blackman

In this paper we introduce the concept of an infinite loop mod $n$ and discuss the properties that these objects have. In particular, we show that a real number $α$ is a counterexa…

A Note on the Base-p Expansions of Putative Counterexamples to the p-adic Littlewood Conjecture

Infinite Loops and the p-adic Littlewood Conjecture. Part I: Reformulating the p-adic Littlewood Conjecture in Terms of Infinite Loops

A Note on the Base- $p$ Expansions of Putative Counterexamples to the $p$ -adic Littlewood Conjecture

Infinite Loops and the $p$ -adic Littlewood Conjecture. Part I: Reformulating the $p$ -adic Littlewood Conjecture in Terms of Infinite Loops