A mild bound |γ_K| ≪ exp((log log |d_K|)^m) on Euler-Kronecker constants along a tower implies the generalized Brauer-Siegel conjecture for that tower; the paper also proves unconditional |γ_K| bounds for almost normal and solvable-closure fields.
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On Euler-Kronecker constants and the generalized Brauer-Siegel conjecture
A mild bound |γ_K| ≪ exp((log log |d_K|)^m) on Euler-Kronecker constants along a tower implies the generalized Brauer-Siegel conjecture for that tower; the paper also proves unconditional |γ_K| bounds for almost normal and solvable-closure fields.