29 citations · 42 across the 3 of their papers we have counts for
5 papers
Greenberg's conjecture for real quadratic number fields
Pietro Mercuri, Maurizio Paoluzi, René Schoof
We compute the -class groups of the fields in the cyclotomic -extensions of the real quadratic fields of discriminant . In all cases the ord…
Modular forms invariant under non-split Cartan subgroups
Pietro Mercuri, Rene Schoof
In this paper we describe a method for computing a basis for the space of weight cusp forms invariant under a non-split Cartan subgroup of prime level . As an application we…
The automorphism group of the non-split Cartan modular curve of level 11
Valerio Dose, Julio Fernández, Josep González +1
We derive equations for the modular curve associated to a non-split Cartan subgroup of . This allows us to compute the automorphism g…
Integral points of a modular curve of level 11
René Schoof, Nikos Tzanakis
Using lower bounds for linear forms in elliptic logarithms we determine the integral points of the modular curve associated to the normalizer of a non-split Cartan group of level 1…
Computing Arakelov class groups
Rene Schoof
Shanks's infrastructure algorithm and Buchmann's algorithm for computing class groups and unit groups of rings of integers of algebraic number fields are most naturally viewed as c…