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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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

Author: Duncan A. Buell
Journal: Math. Comp. 31 (1977), 786-796
MSC: Primary 12A25; Secondary 12A30, 12A70, 12-04
MathSciNet review: 0439802
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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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Article copyright: © Copyright 1977 American Mathematical Society