# Heuristics and conjectures in the direction of a p-adic Brauer-Siegel Theorem

@article{Gras2019HeuristicsAC,
title={Heuristics and conjectures in the direction of a p-adic Brauer-Siegel Theorem},
author={Georges Gras},
journal={Math. Comput.},
year={2019},
volume={88},
pages={1929-1965}
}
• Georges Gras
• Published 12 January 2018
• Mathematics
• Math. Comput.
Let p be a fixed prime number. Let K be a totally real number field of discriminant DK and let TK 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 Cp > 0 such that log(#TK) ≤ Cp · log( √ DK) 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, wearing here…
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