# p-adic Asai L-functions of Bianchi modular forms

## Arithmétique

Lieu:
Salle Kampé de Fériet
Orateur:
Christopher Williams
Affiliation:
Imperial College London
Dates:
Jeudi, 25 Octobre, 2018 - 11:00 - 12:00
Résumé:

The Asai (or twisted tensor) L-function attached to a Bianchi modular form is the restriction to the rationals'' of the standard L-function. Introduced by Asai in 1977, subsequent study has linked its special values to the arithmetic of the corresponding form. In this talk, I will discuss joint work with David Loeffler in which we construct a p-adic Asai L-function for an ordinary weight 2 Bianchi modular form $f$, that is, a measure on $\mathbb{Z}_p^*$ that interpolates the critical values $L^{As}(f,\chi,1)$. The method makes use of techniques from the theory of Euler systems, namely Kato's system of Siegel units, building on the rationality results of Ghate. I will start by giving a brief introduction to p-adic L-functions and Bianchi modular forms.