## Class number in constant extensions of elliptic function fields

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- by James R. C. Leitzel
- Proc. Amer. Math. Soc.
**25**(1970), 183-188 - DOI: https://doi.org/10.1090/S0002-9939-1970-0255516-9
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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 $E$.## References

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## Bibliographic Information

- © Copyright 1970 American Mathematical Society
- 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