Bank–Laine functions, the Liouville transformation and the Eremenko–Lyubich class (2020)
Journal Article
Langley, J. K. (2020). Bank–Laine functions, the Liouville transformation and the Eremenko–Lyubich class. Journal d'Analyse Mathématique, 141(1), 225-246. https://doi.org/10.1007/s11854-020-0115-6

The Bank–Laine conjecture concerning the oscillation of solutions of second order homogeneous linear differential equations has recently been disproved by Bergweiler and Eremenko. It is shown here, however, that the conjecture is true if the set of f... Read More about Bank–Laine functions, the Liouville transformation and the Eremenko–Lyubich class.

Asphericity and finiteness for certain group presentations (2019)
Journal Article
Edjvet, M., & Eljamel, N. (2019). Asphericity and finiteness for certain group presentations. Journal of Algebra, 536, 39-81. https://doi.org/10.1016/j.jalgebra.2019.06.028

We study diagrammatic reducibility for the relative group presentations Rn(k, l, ε) = H, x | t 3 x k t 2 x ε(k+l) where H = t | t n , n ≥ 7, k ≥ 1, l ≥ 0 and ε = ±1. We apply our results to classify finiteness for the group Gn(k, l, ε) defined by Rn(... Read More about Asphericity and finiteness for certain group presentations.