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Proceedings of the American Mathematical Society

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

 

 

Class number in constant extensions of elliptic function fields


Author: James R. C. Leitzel
Journal: Proc. Amer. Math. Soc. 25 (1970), 183-188
MSC: Primary 10.77
DOI: https://doi.org/10.1090/S0002-9939-1970-0255516-9
MathSciNet review: 0255516
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Abstract: For $ F/K$ a function field of genus one having the finite field $ K$ as field of constants and $ E$ the constant extension of degree $ n$ we give explicitly the class number of the field $ E$ as a polynomial expression in terms of the class number of $ F$ and the order of the field $ K$. Applications are made to determine the degree of a constant extension $ E$ necessary to have a predetermined prime $ p$ occur as a divisor of the class number of the field $ E$.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0255516-9
Keywords: Genus one, constant extension, binomial expansions
Article copyright: © Copyright 1970 American Mathematical Society