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 | References | Similar Articles | Additional Information
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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G. Chrystal, A textbook of algebra. Vol. II, A. and C. Black, Edinburgh, 1889; reprint of 6th ed., Chelsea, New York.
- Martin Eichler, Introduction to the theory of algebraic numbers and functions, Pure and Applied Mathematics, Vol. 23, Academic Press, New York-London, 1966. Translated from the German by George Striker. MR 0209258 H. Hasse, Zur Theorie der abstrakten elliptischen Funktionenkörper. I, J. Reine Angew. Math. 175 (1936), 55-62.
- James R. C. Leitzel, Galois cohomology and class number in constant extension of algebraic function fields, Proc. Amer. Math. Soc. 22 (1969), 206–208. MR 242799, DOI https://doi.org/10.1090/S0002-9939-1969-0242799-6
- Edouard Lucas, Theorie des Fonctions Numeriques Simplement Periodiques, Amer. J. Math. 1 (1878), no. 4, 289–321 (French). MR 1505176, DOI https://doi.org/10.2307/2369373
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Additional Information
Keywords:
Genus one,
constant extension,
binomial expansions
Article copyright:
© Copyright 1970
American Mathematical Society