Ha Tran

The size function h0 for a number field is analogous to the dimension of the Riemann-Roch spaces of divisors on an algebraic curve. Van der Geer and Schoof conjectured that h0 attains its maximum at the trivial class of Arakelov divisors if that...

Let F be a number field. The Arakelov class group Pic_0 F of F is an analog to the Picard group of a curve. This group provides us the information of F such as the class number h_F, the class group Cl(F) and the regulator R_F. In this talk, we will...

Reduced ideals of a number field F have inverses of small norms and they form a finite and regularly distributed set in the infrastructure of F. Therefore, they can be used to compute the regulator and the class number of a number field. One usually...