Symmetric power functoriality for holomorphic modular forms
J Newton, JA Thorne - Publications mathématiques de l'IHÉS, 2021 - Springer
Let ff be a cuspidal Hecke eigenform of level 1. We prove the automorphy of the symmetric
power lifting Sym nf Sym^nf for every n≥ 1 n≧1. We establish the same result for a more …
power lifting Sym nf Sym^nf for every n≥ 1 n≧1. We establish the same result for a more …
Symmetric power functoriality for holomorphic modular forms, II
J Newton, JA Thorne - 2021 - repository.cam.ac.uk
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math f</jats: tex-math>< mml: math xmlns: mml=" http://www. w3. org/1998/Math/MathML"> …
math f</jats: tex-math>< mml: math xmlns: mml=" http://www. w3. org/1998/Math/MathML"> …
On the modularity of elliptic curves over imaginary quadratic fields
A Caraiani, J Newton - arXiv preprint arXiv:2301.10509, 2023 - arxiv.org
In this paper, we establish the modularity of every elliptic curve $ E/F $, where $ F $ runs
over infinitely many imaginary quadratic fields, including $\mathbb {Q}(\sqrt {-d}) $ for $ d= 1 …
over infinitely many imaginary quadratic fields, including $\mathbb {Q}(\sqrt {-d}) $ for $ d= 1 …
The Ramanujan and Sato-Tate Conjectures for Bianchi modular forms
We prove the Ramanujan and Sato-Tate conjectures for Bianchi modular forms of weight at
least 2. More generally, we prove these conjectures for all regular algebraic cuspidal …
least 2. More generally, we prove these conjectures for all regular algebraic cuspidal …
Symmetric power functoriality for Hilbert modular forms
J Newton, JA Thorne - arXiv preprint arXiv:2212.03595, 2022 - arxiv.org
arXiv:2212.03595v1 [math.NT] 7 Dec 2022 Page 1 arXiv:2212.03595v1 [math.NT] 7 Dec 2022
SYMMETRIC POWER FUNCTORIALITY FOR HILBERT MODULAR FORMS JAMES NEWTON …
SYMMETRIC POWER FUNCTORIALITY FOR HILBERT MODULAR FORMS JAMES NEWTON …
Lifting and automorphy of reducible mod p Galois representations over global fields
N Fakhruddin, C Khare, S Patrikis - Inventiones mathematicae, 2022 - Springer
We prove the modularity of most reducible, odd representations ̄ ρ: Γ _ Q → GL _2 (k) ρ¯: Γ
Q→ GL 2 (k) with ka finite field of characteristic an odd prime p. This is an analogue of …
Q→ GL 2 (k) with ka finite field of characteristic an odd prime p. This is an analogue of …
A pp‐adic approach to the existence of level‐raising congruences
JA Thorne - Proceedings of the London Mathematical Society, 2024 - Wiley Online Library
We construct level‐raising congruences between pp‐ordinary automorphic representations,
and apply this to the problem of symmetric power functoriality for Hilbert modular forms. In …
and apply this to the problem of symmetric power functoriality for Hilbert modular forms. In …
Congruences between modular forms
JA Thorne - Proceedings-Mathematical Sciences, 2024 - Springer
We survey the connections between modular forms and representations of Galois groups
that are predicted by the Langlands programme. We focus in particular on the applications of …
that are predicted by the Langlands programme. We focus in particular on the applications of …
Symplectic determinant laws and invariant theory
We introduce the notion of $\textit {symplectic determinant laws} $ by analogy with
Chenevier's definition of determinant laws. Symplectic determinant laws are a way to define …
Chenevier's definition of determinant laws. Symplectic determinant laws are a way to define …
On deformation rings of residual Galois representations with three Jordan-Holder factors and modularity
X Huang - arXiv preprint arXiv:2308.02708, 2023 - arxiv.org
In this paper, we study Fontaine-Laffaille, self-dual deformations of a mod p non-semisimple
Galois representation of dimension n with its Jordan-Holder factors being three mutually non …
Galois representation of dimension n with its Jordan-Holder factors being three mutually non …