Abstract
We find a lower bound on the number of real quadratic fields whose class groups have an element of order 3. More precisely, we show that the number of real quadratic fields whose absolute discriminant is \(\le x\) and whose class number is divisible by 3 is \(\gg x^{\frac{15}{16}}\) improving the existing best known lower bound \(\gg x^{\frac{7}{8}}\) of Byeon and Koh. We also prove that the class number of the imaginary quadratic field \({\mathbb {Q}} ( {\sqrt{-q} }),\) for certain values of q, is divisible by 3.
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Both the author’s would like to thank UGC for financial support.
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Hoque, A., Saikia, H.K. A note on quadratic fields whose class numbers are divisible by 3. SeMA 73, 1–5 (2016). https://doi.org/10.1007/s40324-015-0051-z
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DOI: https://doi.org/10.1007/s40324-015-0051-z