Panagiotis Tsaknias

activity

20122018

most citedGenuine Bianchi modular forms of higher level, at varying weight and discriminant

6 citations · 8 across the 8 of their papers we have counts for

collaborators

9 papers

math.NT2018

On the number of Galois orbits of newforms

Luis Dieulefait, Ariel Pacetti, Panagiotis Tsaknias

Counting the number of Galois orbits of newforms in $S_{k} (Γ_{0} (N))$ and giving some arithmetic sense to this number is an interesting open problem. The case $N = 1$ corresponds to Maed…

math.NT2017★ 6 cited

Genuine Bianchi modular forms of higher level, at varying weight and discriminant

Alexander Rahm, Panagiotis Tsaknias

Bianchi modular forms are automorphic forms over an imaginary quadratic field, associated to a Bianchi group. Even though modern studies of Bianchi modular forms go back to the mid…

math.NT2016

Topics on modular Galois representations modulo prime powers

Panagiotis Tsaknias, Gabor Wiese

This article surveys modularity, level raising and level lowering questions for two-dimensional representations modulo prime powers of the absolute Galois group of the rational num…

math.NT2016★ 1 cited

Possible connection between a generalized Maeda's conjecture and local types

Luis Dieulefait, Panagiotis Tsaknias

Here we follow on the proposed generalization of Maeda's conjecture made in [2]. We report on computations that suggest a relation between the number of local types and the number…

math.NT2014

Criteria for p-ordinarity of families of elliptic curves over infinitely many number fields

Nuno Freitas, Panagiotis Tsaknias

Let $K_{i}$ be a number field for all $i \in Z_{> 0}$ and let $E$ be a family of elliptic curves containing infinitely many members defined over $K_{i}$ for all $i$ .…

math.NT2013★ 1 cited

Dimension Formulae for Spaces of Lifted Bianchi Modular Forms

Mehmet Haluk Sengun, Panagiotis Tsaknias

In this note, we work out the dimension of the subspace of base-change forms and their twists inside the space of Bianchi modular forms with fixed (Galois stable) level and weight.

math.NT2012

A characterization of ordinary modular eigenforms with CM

Rajender Adibhatla, Panagiotis Tsaknias

For a rational prime $p \geq 3$ we show that a $p$ -ordinary modular eigenform $f$ of weight $k \geq 2$ , with $p$ -adic Galois representation $ρ_{f}$ , mod $p^{m}$ reductions $ρ_{f, m}$ ,…

math.NT2012

A possible generalization of Maeda's conjecture

Panagiotis Tsaknias

We report on observations we made on computational data that suggest a generalization of Maeda's conjecture regarding the number of Galois orbits of newforms of level $N = 1$ , to h…

math.NT2012

A level raising result for modular Galois representations modulo prime powers

Panagiotis Tsaknias

In this work we provide a level raising theorem for $mod λ^{n}$ modular Galois representations. It allows one to see such a Galois representation that is modular of level $N$ , weigh…