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Mathematics of Computation

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



On the $ 3$-rank of quadratic fields and the Euler product

Authors: Carol Neild and Daniel Shanks
Journal: Math. Comp. 28 (1974), 279-291
MSC: Primary 12A25; Secondary 12A65
MathSciNet review: 0352042
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Abstract: This paper covers many (closely related) topics: the distribution of the 3-Sylow subgroups of imaginary quadratic fields; the possibility of finding 3-ranks greater than 4; some questions concerning $ {a^3} = {b^2} + {c^2}D$; and the convergence of Euler products and its relation to the extended Riemann hypothesis. Two programs that were used in this investigation are described.

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Article copyright: © Copyright 1974 American Mathematical Society