Zobrazeno 1 - 10
of 24
pro vyhledávání: '"Tsaknias, Panagiotis"'
Counting the number of Galois orbits of newforms in $S_k(\Gamma_0(N))$ and giving some arithmetic sense to this number is an interesting open problem. The case $N=1$ corresponds to Maeda's conjecture (still an open problem) and the expected number of
Externí odkaz:
http://arxiv.org/abs/1805.10361
Autor:
Rahm, Alexander, Tsaknias, Panagiotis
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 1960's, most of the fundamental problems surrounding their theory are
Externí odkaz:
http://arxiv.org/abs/1703.07663
Autor:
Tsaknias, Panagiotis, Wiese, Gabor
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 numbers. It contributes some new results and describes algorithms and a d
Externí odkaz:
http://arxiv.org/abs/1612.05017
Autor:
Dieulefait, Luis, Tsaknias, Panagiotis
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 of non-CM newform Galois orbits. We extend the conjecture into spaces
Externí odkaz:
http://arxiv.org/abs/1608.05285
Autor:
Freitas, Nuno, Tsaknias, Panagiotis
Let $K_i$ be a number field for all $i \in \mathbb{Z}_{> 0}$ and let $\mathcal{E}$ be a family of elliptic curves containing infinitely many members defined over $K_i$ for all $i$. Fix a rational prime $p$. We give sufficient conditions for the exist
Externí odkaz:
http://arxiv.org/abs/1404.3278
Publikováno v:
Journal de Théorie des Nombres de Bordeaux, 2019 Jan 01. 31(1), 27-48.
Externí odkaz:
https://www.jstor.org/stable/26730885
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.
Externí odkaz:
http://arxiv.org/abs/1310.5385
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 $\rho_f$, mod ${p^m}$ reductions $\rho_{f,m}$, and with complex multiplication (CM), is characterized by the ex
Externí odkaz:
http://arxiv.org/abs/1206.0177
Autor:
Tsaknias, Panagiotis
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 higher levels. They also suggest a possible formula for this number in
Externí odkaz:
http://arxiv.org/abs/1205.3420