3 papers
math.NT2025
Evaluation of Bianchi Rigid Meromorphic Cocycles at Big ATR Points
Lennart Gehrmann, Xavier Guitart, Marc Masdeu
We develop the tools required to effectively evaluate the Bianchi rigid meromorphic cocycles introduced by Darmon-Gehrmann-Lipnowski at big ATR points, and use them to obtain the f…
math.NT2025
Periods of modular forms and applications to the conjectures of Oda and of Prasanna-Venkatesh
Xavier Guitart, Santiago Molina
We establish several formulas relating periods of modular forms on quaternion algebras over number fields to special values of L-functions. Our main inputs are the cohomological te…
math.NT2025
Abelian varieties genuinely of -type
Francesc Fité, Enric Florit, Xavier Guitart
A simple abelian variety defined over a number field is called of -type if there exists a number field of degree which is a subalgebra of $\math…