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#### Seminar der Forschergruppe 'Symmetrie, Geometrie und Arithmetik'

„p-adic Asai L-functions of Bianchi modular forms“
Dr. Chris Williams, Imperial College London

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 - that is, a measure on $\mathbb{Z}_p^*$ that interpolates the critical values $L^{As}(f,\chi,1)$ - for ordinary weight 2 Bianchi modular forms. 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 begin by giving a brief introduction to $p$-adic $L$-functions and Bianchi modular forms.

Freitag, den 26. Januar 2018 um 13:30 Uhr, in INF205, SR A Freitag, den 26. Januar 2018 at 13:30, in INF205, SR A

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Michael Fütterer