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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Class number in constant extensions of function fields


Author: James R. C. Leitzel
Journal: Proc. Amer. Math. Soc. 36 (1972), 47-54
MSC: Primary 12A90
DOI: https://doi.org/10.1090/S0002-9939-1972-0308085-0
MathSciNet review: 0308085
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Abstract: Let $ F/K$ be a function field in one variable of genus g having the finite field K as exact field of constants. Suppose p is a rational prime not dividing the class number of F. In this paper an upper bound is derived for the degree of a constant extension E necessary to have p occur as a divisor of the class number of the field E.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0308085-0
Keywords: Zeta function, constant extension, reciprocal polynomials
Article copyright: © Copyright 1972 American Mathematical Society