Analysis of harmonic numbers and matrix equations for two-dimensional Galois representations, suggesting new insights for mathematical solutions.
We evaluate some determinants involving harmonic numbers that are needed in order to provide solutions to certain matrix equations occurring in our earlier paper {CG24}. That paper determined the mod p reductions of all two-dimensional semi-stable representations Vk,L of the Galois group of Qₚ of weights 3 ≤ k ≤ p+1 and L-invariants L for primes p ≥ 5. The present paper computes these determinants with the aid of two computer packages.
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Chitrao et al. (2026) studied this question.
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