For a given positive integer k, we prove that there are at least x1/2-o(1) integers d ≤ x such that the real quadratic fields ℚ(√ d + 1), ⋯ ,ℚ(√ d + k) have class numbers essentially as large as possible..
Consecutive Real Quadratic Fields with Large Class Numbers
Cherubini, Giacomo;Fazzari, Alessandro;
2022-01-01
Abstract
For a given positive integer k, we prove that there are at least x1/2-o(1) integers d ≤ x such that the real quadratic fields ℚ(√ d + 1), ⋯ ,ℚ(√ d + k) have class numbers essentially as large as possible..
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