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

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

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 …