Inventiones mathematicae

, Volume 98, Issue 3, pp 599–622 | Cite as

Analytic formulas for the regulator of a number field

  • Eduardo Friedman


LetR=Rk andw=wk be the regulator and the number of roots of unity in the number fieldk. We determine allk for whichR/w<1/8. There are nine such fields. Sincew≥2, we have allk withR<1/4. In particular, we find the first three minima ofR over allk. There are three main ingredients to the proof:
  1. i)

    A new analytic formula (Theorem A below).

  2. ii)

    A refinement of Remak's geometric approach.

  3. iii)

    A refinement of Zimmert's analytic method.



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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Eduardo Friedman
    • 1
  1. 1.Department of MathematicsUniversity of PennsylvaniaPhiladelphiaUSA

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