Lower bounds for class numbers of real quadratic fields

Mollin, R. A.

doi:10.1090/S0002-9939-1986-0826478-X

Lower bounds for class numbers of real quadratic fields
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Proc. Amer. Math. Soc. 96 (1986), 545-550 Request permission

Abstract:

Based on the fundamental units of real quadratic fields we provide lower bounds for their class numbers. These results extend work of H. Hasse [2] and generalize and correct results of H. Yokoi [8, 9]. Moreover, for certain real quadratic fields we provide criteria for their class numbers to be divisible by a specific integer.

References

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Helmut Hasse, Über mehrklassige, aber eingeschlechtige reell-quadratische Zahlkörper, Elem. Math. 20 (1965), 49–59 (German). MR 191889
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Sur la resolution des equations

Hideo Yokoi, On real quadratic fields containing units with norm $-1$, Nagoya Math. J. 33 (1968), 139–152. MR 233803
Hideo Yokoi, On the fundamental unit of real quadratic fields with norm $1$, J. Number Theory 2 (1970), 106–115. MR 252351, DOI 10.1016/0022-314X(70)90010-7