Eduardo Friedman

Analytic formulas for the regulator of a number field

SummaryLetR=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:i)A new analytic formula (Theorem A below).ii)A refinement of Remaks geometric approach.iii)A refinement of Zimmerts analytic method.

Signed fundamental domains for totally real number fields

We give a signed fundamental domain for the action on

Computing the residue of the Dedekind zeta function

\mathbb{R}^n_+

Regulators and total positivity

of the totally positive units

A POISSON SUMMATION FORMULA FOR EXTENSIONS OF NUMBER FIELDS

E_+

On the l -adic Iwasawa l-invariant in a p -extension

of a totally real number field

On the -adic Iwasawa -invariant in a -extension

k

The smallest arithmetic hyperbolic three-orbifold

of degree

AN EMBEDDING THEOREM FOR QUATERNION ALGEBRAS

n

Shintani¿Barnes zeta and gamma functions

. The domain