3 papers
math.NT2025
Proof of the Lehmer conjecture on Ramanujan's function
Minjia Shi, Lu Wang, Patrick Solé
A criterion for Lehmer's conjecture in terms of the spherical designs held in the shells of the lattice was derived by de La Harpe, Pache and Venkov circa 2005. We check that…
cs.IT2025
Disproving some theorems in Sharma and Chauhan et al. (2018, 2021)
Ramy Takieldin, Patrick Solé
The main objective of this work is to show, through counterexamples, that some of the theorems presented in the papers of Sharma \textit{et al.} (2018) and Chauhan \textit{et al.}…
cs.IT2024
Some -designs invariant under
Minjia Shi, Ruowen Liu, Patrick Solé
We construct a ternary [49,25,7] code from the row span of a Jacobsthal matrix. It is equivalent to a Generalized Quadratic Residue (GQR) code in the sense of van Lint and MacWilli…