Class number in constant extensions of function fields
HTML articles powered by AMS MathViewer
- by James R. C. Leitzel PDF
- Proc. Amer. Math. Soc. 36 (1972), 47-54 Request permission
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.References
- William Snow Burnside and Arthur William Panton, The theory of equations: With an introduction to the theory of binary algebraic forms, Dover Publications, Inc., New York, 1960. 2 volumes. MR 0115987
- 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
- 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 10.1090/S0002-9939-1969-0242799-6 B. L. van der Waerden, Moderne Algebra. Vol. 1, 2nd rev. ed., English transl., Ungar, New York, 1953.
Additional Information
- © Copyright 1972 American Mathematical Society
- 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