Computing Stark units for totally real cubic fields

Computing Stark units for totally real cubic fields

A method for computing provably accurate values of partial zeta functions is used to numerically confirm the rank one abelian Stark Conjecture for some totally real cubic fields of discriminant less than 50000. The results of these computations are used to provide explicit Hilbert class fields and some ray class fields for the cubic extensions.

Gross–Stark units for totally real number fields

Shintani zeta-functions and Gross–Stark units for totally real fields

Let F be a totally real number field and let p be a finite prime of F , such that p splits completely in the finite abelian extension H of F . Stark has proposed a conjecture stating the existence of a p-unit in H with absolute values at the places above p specified in terms of the values at zero of the partial zeta-functions associated to H/F . Gross proposed a refinement of Stark’s conjecture...

Gross–stark Units, Stark–heegner Points, and Class Fields of Real Quadratic Fields

Gross–Stark units, Stark–Heegner points, and class fields of real quadratic fields by Samit Dasgupta Doctor of Philosophy in Mathematics University of California, Berkeley Professor Kenneth Ribet, Chair We present two generalizations of Darmon’s construction of Stark–Heegner points on elliptic curves defined overQ. First, we provide a lifting of Stark–Heegner points from elliptic curves to cert...

On Totally Real Cubic Fields with Discriminant D < 107

The authors have constructed a table of the 592923 nonconjugate totally real cubic number fields of discriminant D < 107, thereby extending the existing table of fields with D < 5 x 105 constructed by Ennola and Turunen [4]. Each field is given by its discriminant and the coefficients of a generating polynomial. The method used is an improved version of the method developed in [8]. The article ...