A note on Greenberg’s conjecture and the abc conjecture

Ichimura, Humio

doi:10.1090/S0002-9939-98-04196-3

A note on Greenberg’s conjecture and the abc conjecture
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by Humio Ichimura

Proc. Amer. Math. Soc. 126 (1998), 1315-1320

DOI: https://doi.org/10.1090/S0002-9939-98-04196-3

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Abstract:

For any totally real number field $k$ and any prime number $p$, Greenberg’s conjecture for $(k,p)$ asserts that the Iwasawa invariants $\lambda _p(k)$ and $\mu _p(k)$ are both zero. For a fixed real abelian field $k$, we prove that the conjecture is “affirmative” for infinitely many $p$ (which split in $k)$ if we assume the abc conjecture for $k$.

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