GENUS FIELDS OF CYCLIC l-EXTENSIONS OF RATIONAL FUNCTION FIELDS
2013 ◽
Vol 09
(05)
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pp. 1249-1262
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We give a construction of genus fields for Kummer cyclic l-extensions of rational congruence function fields, l a prime number. First we find this genus field for a field contained in a cyclotomic function field using Leopoldt's construction by means of Dirichlet characters and the Hilbert class field defined by Rosen. The general case follows from this. This generalizes the result obtained by Peng for a cyclic extension of degree l.
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1974 ◽
Vol 189
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pp. 77-77
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2014 ◽
Vol 150
(4)
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pp. 507-522
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2020 ◽
Vol 16
(05)
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pp. 1081-1109
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2014 ◽
Vol 10
(08)
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pp. 2187-2204
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2004 ◽
pp. 271-286
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