M. Valentino · wovepaper

activity

20172020

collaborators

6 papers

Atkin-Lehner theory for Drinfeld modular forms and applications

Maria Valentino

The present paper deals with Atkin-Lehner theory for Drinfeld modular forms. We provide an equivalent definition of $p$ -newforms (which makes computations easier) and co…

On Drinfeld cusp forms of prime level

Andrea Bandini, Maria Valentino

Let $(P_{d})$ be any prime of $F_{q} [t]$ of degree $d$ and consider the space of Drinfeld cusp forms of level $P_{d}$ , i.e. for the modular group $Γ_{0} (P_{d})$ . We provide a defini…

On the structure and slopes of Drinfeld cusp forms

Andrea Bandini, Maria Valentino

We define oldforms and newforms for Drinfeld cusp forms of level $t$ and conjecture that their direct sum is the whole space of cusp forms. Moreover we describe explicitly the matr…

On the Atkin $U_{t}$ -operator for $Γ_{0} (t)$ -invariant Drinfeld cusp forms

Andrea Bandini, Maria Valentino

We study the diagonalizability of the Atkin $U_{t}$ -operator acting on Drinfeld cusp forms for $Γ_{0} (t)$ : starting with the slopes of eigenvalues and then moving to the space of cusp…

On the Atkin $U_{t}$ -operator for $Γ_{1} (t)$ -invariant Drinfeld cusp forms

Andrea Bandini, Maria Valentino

We study the diagonalizability of the Atkin $U_{t}$ -operator acting on Drinfeld cusp forms for $Γ_{1} (t)$ and $Γ (t)$ using Teitelbaum's interpretation as harmonic cocycles. For small w…

Euler characteristic and Akashi series for Selmer groups over global function fields

Andrea Bandini, Maria Valentino

Let $A$ be an abelian variety defined over a global function field $F$ of positive characteristic $p$ and let $K / F$ be a $p$ -adic Lie extension with Galois group $G$ . We provide a…