Fundamental units in a parametric family of not totally real quintic number fields
نویسندگان
چکیده
In this article we compute fundamental units for a family of number fields generated by a parametric polynomial of degree 5 with signature (1, 2) and Galois group D5.
منابع مشابه
Quintic Polynomials and Real Cyclotomic Fields with Large Class Numbers
We study a family of quintic polynomials discoverd by Emma Lehmer. We show that the roots are fundamental units for the corresponding quintic fields. These fields have large class numbers and several examples are calculated. As a consequence, we show that for the prime p = 641491 the class number of the maximal real subfield of the pth cyclotomic field is divisible by the prime 1566401. In an a...
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In [Leh], Emma Lehmer constructed a parametric family of units in real quintic fields of prime conductor p = t + 5t + 15t + 25t+ 25, as translates of Gaussian periods. Later, Schoof and Washington [SW] showed that these units were fundamental units. In this note, we observe that Lehmer’s family comes from the covering of modular curves X1(25) −→ X0(25). This gives a conceptual explanation for t...
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