Under the stated conditions on p and q, the Iwasawa λ-invariant of the cyclotomic ℤ₂-extension of K = ℚ(√(pq)) is zero.
Sands, On the non-triviality of the basic Iwasawa -invariant for an infinitude of imaginary quadratic fields, Acta Arith
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In Z_p-extensions of totally p-adic imaginary quadratic fields, the p-valuation of a Fermat quotient of the fundamental p-unit governs the orders of logarithmic class groups and the quotients of the first two layers of p-class group filtrations for large n.
citing papers explorer
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On the Iwasawa $\lambda$-invariant of the cyclotomic $\mathbb{Z}_2$-extension of a family of real quadratic fields in which $2$ splits
Under the stated conditions on p and q, the Iwasawa λ-invariant of the cyclotomic ℤ₂-extension of K = ℚ(√(pq)) is zero.
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On the $\mathbb{Z}_p$-extensions of a totally $p$-adic imaginary quadratic field -- With an appendix by Jean-Fran\c{c}ois Jaulent
In Z_p-extensions of totally p-adic imaginary quadratic fields, the p-valuation of a Fermat quotient of the fundamental p-unit governs the orders of logarithmic class groups and the quotients of the first two layers of p-class group filtrations for large n.