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Journal Article

Small Class Numbers and Extreme Values of $L$-Functions of Quadratic Fields

Duncan A. Buell
Mathematics of Computation
Vol. 31, No. 139 (Jul., 1977), pp. 786-796
DOI: 10.2307/2006012
Stable URL: http://www.jstor.org/stable/2006012
Page Count: 11
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Small Class Numbers and Extreme Values of $L$-Functions of Quadratic Fields
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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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