# 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} }

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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