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On the Class Numbers of the Maximal Real Subfields of Cyclotomic Function Fields, II

✍ Scribed by Humio Ichimura

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
229 KB
Volume
72
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let q be a power of a prime number p and k=F q (T ) the rational function field with a fixed indeterminate T. For an irreducible monic P=P(T ) in R=F q [T], let k(P) + be the maximal real subfield of the P th cyclotomic function field and h + T (P) the class number of k(P) + associated to R. We prove that there exist infinitely many irreducible monics P in R with p | h + T (P) under some assumptions on q.

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