Small class numbers and extreme values of 𝐿-functions of quadratic fields

Buell, Duncan A.

doi:10.1090/S0025-5718-1977-0439802-X

Small class numbers and extreme values of $L$-functions of quadratic fields
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Math. Comp. 31 (1977), 786-796 Request permission

Abstract:

The table of class numbers h of imaginary quadratic fields described in [1] was placed on magnetic tape. This tape was then processed to find the occurrences of $h \leqslant 125$ and to find the successive extreme values of the Dirichlet L-functions $L(1,{\chi _{ - D}})$, ${\chi _{ - D}}$ the Kronecker symbol of the field $Q(\sqrt { - D} )$ of discriminant - D. A comparison was made between the observed extrema and the bounds obtained for the L-functions by Littlewood [5] assuming Riemann hypotheses.

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