On an upper bound of 𝜆-invariants of ℤ_𝑝-extensions over an imaginary quadratic field

Abstract

For an odd prime number 𝑝, we give an explicit upper bound of 𝜆-invariants for all ℤ_𝑝-extensions of an imaginary quadratic field 𝑘 under several assumptions. We also give an explicit upper bound of 𝜆-invariants for all ℤ_𝑝-extensions of 𝑘 in the case where the 𝜆-invariant of the cyclotomic ℤ_𝑝-extension of 𝑘 is equal to 3.