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Responsabili:

Nel calendario si indicano i seminari di geometria algebrica e altre attività di interesse, organizzate dall'Università e dal Politecnico di Torino.

## Evento

Titolo: Interpolation properties of power series expansions of modular forms
Quando: 11/04/2018 - 15:00
Dove: Palazzo Campana - TORINO
Aula: Aula C
Relatore: Andrea Mori
Afferenza: Università di Torino
Locandina:

## Descrizione:

Abstract: Let $f$ be a classical modular cuspform of weight $k$ and level $N$ defined over a ring $B$ of $p$-adic integers and let $x$ be a $B$-rational CM-point
in the corresponding modular or Shimura scheme of arithmetic level $N$. When the abelian variety corresponding to $x$ has ordinary reduction mod $p$
we define a power series expansion of $f$ around $x$ with coefficients in some bigger $p$-adic ring $B^\prime$. By Mahler’s theory this power series defines
a measure $\mu_x$ on $\mathbb{Z}_p$ with values in $B^\prime$. By letting $x$ vary in its Galois orbit the measures $\mu_x$ can added together to form a
new measure $\mu$. The squares of the moments of $\mu$ are related via the theory of Harris-Kudla to the special value of a twisted $L$-function
attached to $f$ and the CM field $K$. Moreover, when $f$ is eigen for the Hecke $T_p$-operator we compute the correct interpolation factor for the restriction of
$\mu$ to $\mathbb{Z}_p^\times$.

## Sede

Sede:
Indirizzo: Via Carlo Alberto 10
CAP: 10123
Città: TORINO