4 citations · 6 across the 6 of their papers we have counts for
8 papers
Arithmetic intersections on non-split Cartan modular curves
Jonathan Love, Elie Studnia, Jan Vonk
Let be a prime number, and let be two coprime fundamental discriminants. When splits in and the height pairi…
Congruences modulo to are trivial
Elie Studnia
We say that two elliptic curves and over are congruent modulo a prime if their -torsion Galois modules (over the algebraic closure of ) are…
Compactified moduli spaces and Hecke correspondences for elliptic curves with a prescribed -torsion scheme
Elie Studnia
Given an integer , we prove that for any ring and any finite locally free commutative -group scheme whose geometric fibres are isomorphic to the -torsion su…
L-functions and rational points for Galois twists of modular curves
Elie Studnia
Let be an odd prime and be a rational elliptic curve. There is a smooth affine curve whose rational points parametrize elliptic curves su…
On obstructions to the Euler system method for Rankin-Selberg convolutions
Elie Studnia
To apply the Euler system method to a -adic Galois representation , one needs the existence of a such that is free of rank on…
Refined Selmer equations for the thrice-punctured line in depth two
Alex J. Best, L. Alexander Betts, Theresa Kumpitsch +5
In [Kim05], Kim gave a new proof of Siegel's Theorem that there are only finitely many -integral points on . One advantage of Kim…
Quantum ergodicity for pseudo-Laplacians
Elie Studnia
We prove quantum ergodicity for the eigenfunctions of the pseudo-Laplacian on Riemannian surfaces with finitely many hyperbolic cusps and ergodic geodesic flow.
Quantum Limits for Harmonic Oscillator
Elie Studnia
In this note we consider high energy eigenfunctions of the harmonic oscillator in and prove that any invariant measure on the energy surface can be written as a weak…