Number Theory Related to Fermat’s Last Theorem pp 321-340 | Cite as

# Elliptic Units in Function Fields

Chapter

## Abstract

In [R], Robert uses modular functions to construct units in the class fields H of an imaginary quadratic number field F. In case H/F has prime power conductor, he computes the index of these “elliptic units” in the full unit group of H and finds that, up to trivial factors, the index is the class number of H. He therefore refers to his results on indices as *class number formulas*.

## Keywords

Prime Ideal Galois Group Class Number Positive Element Class Field
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## References

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*J. of Number Theory.*Google Scholar - [Hl]D. Hayes. “Explicit Class Field Theory in Global Function Fields,”
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*Bull. Soc. Math. France*, Mem. No. 36 (1973).Google Scholar - [Ros]M. Rosen. “S-Units and S-Class Group in Algebraic Function Fields,”
*J. Algebra*26 (1973), 98–108.CrossRefGoogle Scholar - [S]W. Sinnott. “On the Stiekel berger Ideal and Circular Units of a Cyclotomic Field,”
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© Springer Science+Business Media New York 1982