• Mathematics
• Published 2018

# Heuristics in direction of a p-adic Brauer--Siegel theorem

@inproceedings{Gras2018HeuristicsID,
title={Heuristics in direction of a p-adic Brauer--Siegel theorem},
author={Georges Gras},
year={2018}
}
Let p be a fixed prime number. Let K be a totally real number field of discriminant D_K and let T_K be the torsion group of the Galois group of the maximal abelian p-ramified pro-p-extension of K (under Leopoldt's conjecture). We conjecture the existence of a constant C_p>0 such that log(#T_K) ≤ C_p log(\sqrt(D_K)) when K varies in some specified families (e.g., fields of fixed degree). In some sense, we suggest the existence of a p-adic analogue, of the classical Brauer--Siegel Theorem… CONTINUE READING
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