Jaitra Chattopadhyay, A. Saikia

Dec 1, 2021

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Journal

The Ramanujan Journal

Abstract

For a prime number p ≥ 5, we explicitly construct a family of imaginary quadratic fields K with ideal class groups ClK having p-rank rkp(ClK) at least 2. We also quantitatively prove, under the assumption of the abc-conjecture, that for sufficiently large positive real numbers X and any real number ε with 0 < ε < 1 p−1 , the number of imaginary quadratic fields K with the absolute value of the discriminant dK ≤ X and rkp(ClK) ≥ 2 is ≫ X 1 p−1 . This improves the previously known lower bound of X 1 p −ε due to Byeon and the recent bound X 1 p /(logX) due to Kulkarni and Levin.

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