Title: Triviality of the ℓ-class groups in -extensions of for split primes <i>p</i> ≡ 1 modulo 4
Abstract: Abstract In this paper we study the class numbers in the finite layers of certain non-cyclotomic $\mathbb{Z}$ p -extensions of the imaginary quadratic field $\mathbb{Q}(\sqrt{-1})$ , for all primes p ≡ 1 modulo 4. By studying the Mahler measure of elliptic units, we are able to show that there are only finitely many primes ℓ congruent to a primitive root modulo p 2 that divide any of the class numbers in the $\mathbb{Z}$ p -extension.
Publication Year: 2014
Publication Date: 2014-05-12
Language: en
Type: article
Indexed In: ['crossref']
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