Ariel Weiss

activity

20182026

most citedOn the images of Galois representations attached to low weight Siegel modular forms

12 citations · 28 across the 10 of their papers we have counts for

collaborators

12 papers

math.NT2026

Experiments on $3$ -isogeny Selmer groups of elliptic curves with a $3$ -torsion point

Ariel Weiss, Dongchen Zou

Let $E_{A, B} : y^{2} + A x y + B y = x^{3}$ be an elliptic curve over $Q$ . The $3$ -torsion point $(0, 0)$ induces a $3$ -isogeny $ϕ : E_{A, B} \to E_{A, B}^{'}$ . Assuming $E_{A,B}…

math.NT2025

Distinguishing Siegel modular forms

Arvind Kumar, Ariel Weiss

Let $f$ and $f^{'}$ be genus $2$ cuspidal Siegel paramodular newforms. We prove that if their Hecke eigenvalues $a_{p}$ and $a_{p}^{'}$ satisfy a non-trivial polynomial relation $P(a_p, a_p'…

math.NT2024

Polylogarithmic motivic Chabauty-Kim for $P^{1} ∖ {0, 1, \infty}$ : the geometric step via resultants

David Jarossay, David T. -B. G. Lilienfeldt, Francesco Maria Saettone +2

Given a finite set $S$ of distinct primes, we propose a method to construct polylogarithmic motivic Chabauty-Kim functions for $P^{1} ∖ {0, 1, \infty}$ using resul…

math.NT2024

Five-dimensional compatible systems and the Tate conjecture for elliptic surfaces

Lian Duan, Xiyuan Wang, Ariel Weiss

Let $(ρ_{λ} : G_{Q} \to GL_{5} (E_{λ}))_{λ}$ be a strictly compatible system of Galois representations such that no Hodge--Tate weight has multiplicity…

math.NT2024

Maximal stable lattices in representations over discretely valued fields

Amit Ophir, Ariel Weiss

Let $ρ : G \to GL_{n} (K)$ be an continuous irreducible representation of a compact group over a complete discretely valued field $K$ . Let $W_{i}, W_{j}$ be two irreducible sub…

math.NT2022★ 1 cited

On the Lang--Trotter conjecture for Siegel modular forms

Arvind Kumar, Moni Kumari, Ariel Weiss

Let $f$ be a genus two cuspidal Siegel modular eigenform. We prove an adelic open image theorem for the compatible system of Galois representations associated to $f$ , generalising…

math.NT2021★ 7 cited

Rank growth of elliptic curves over $N$ -th root extensions

Ari Shnidman, Ariel Weiss

Fix an elliptic curve $E$ over a number field $F$ and an integer $n$ which is a power of $3$ . We study the growth of the Mordell--Weil rank of $E$ after base change to the fields $…

math.NT2021

On Ribet's Lemma for $GL_{2}$ modulo prime powers

Amit Ophir, Ariel Weiss

Let $ρ : G \to GL_{2} (K)$ be a continuous representation of a compact group $G$ over a complete discretely valued field $K$ , with ring of integers $O$ and unifor…

math.NT2021★ 3 cited

Ranks of abelian varieties in cyclotomic twist families

Ari Shnidman, Ariel Weiss

Let $A$ be an abelian variety over a number field $F$ , and suppose that $Z [ζ_{n}]$ embeds in $End_{F ˉ} A$ , for some root of unity $ζ_{n}$ of order $n = 3^{m}$ . Assum…

math.NT2021★ 5 cited

Elements of prime order in Tate-Shafarevich groups of abelian varieties over $Q$

Ari Shnidman, Ariel Weiss

For each prime $p$ , we show that there exist geometrically simple abelian varieties $A / Q$ with non-trivial $p$ -torsion in their Tate-Shafarevich groups. Specifically, for a…

math.NT2020

Lafforgue pseudocharacters and parities of limits of Galois representations

Tobias Berger, Ariel Weiss

Let $F$ be a CM field with totally real subfield $F^{+}$ and let $π$ be a $C$ -algebraic cuspidal automorphic automorphic representation of $U (a, b) (A_{F^{+}})$ whose a…

math.NT2018★ 12 cited

On the images of Galois representations attached to low weight Siegel modular forms

Ariel Weiss

Let $π$ be a cuspidal automorphic representation of $GSp_{4} (A_{Q})$ , whose archimedean component is a holomorphic discrete series or limit of discrete series represe…

Experiments on 3-isogeny Selmer groups of elliptic curves with a 3-torsion point

Distinguishing Siegel modular forms

Polylogarithmic motivic Chabauty-Kim for P1∖{0,1,∞}: the geometric step via resultants

Five-dimensional compatible systems and the Tate conjecture for elliptic surfaces

Maximal stable lattices in representations over discretely valued fields

On the Lang--Trotter conjecture for Siegel modular forms

Rank growth of elliptic curves over N-th root extensions

On Ribet's Lemma for GL2​ modulo prime powers

Ranks of abelian varieties in cyclotomic twist families

Elements of prime order in Tate-Shafarevich groups of abelian varieties over Q

Lafforgue pseudocharacters and parities of limits of Galois representations

On the images of Galois representations attached to low weight Siegel modular forms

Experiments on $3$ -isogeny Selmer groups of elliptic curves with a $3$ -torsion point

Polylogarithmic motivic Chabauty-Kim for $P^{1} ∖ {0, 1, \infty}$ : the geometric step via resultants

Rank growth of elliptic curves over $N$ -th root extensions

On Ribet's Lemma for $GL_{2}$ modulo prime powers

Elements of prime order in Tate-Shafarevich groups of abelian varieties over $Q$