Manuel Luethi
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View article: Measure rigidity and equidistribution for fractal carpets
Measure rigidity and equidistribution for fractal carpets Open
Let $θ$ be a Bernoulli measure which is stationary for a random walk generated by finitely many contracting rational affine dilations of $\mathbb{R}^d$, and let $\mathcal{K} = \mathrm{supp}(θ)$ be the corresponding attractor. An example in…
View article: Simultaneous supersingular reductions of CM elliptic curves
Simultaneous supersingular reductions of CM elliptic curves Open
We study the simultaneous reductions at several supersingular primes of elliptic curves with complex multiplication. We show – under additional congruence assumptions on the CM order – that the reductions are surjective (and even become eq…
View article: Random Walks, Spectral Gaps, and Khintchine's Theorem on Fractals
Random Walks, Spectral Gaps, and Khintchine's Theorem on Fractals Open
This work addresses problems on simultaneous Diophantine approximation on fractals, motivated by a long standing problem of Mahler regarding Cantor's middle $1/3$ set. We obtain the first instances where a complete analogue of Khintchine's…
View article: Primitive rational points on expanding horocycles in products of the modular surface with the torus
Primitive rational points on expanding horocycles in products of the modular surface with the torus Open
We prove effective equidistribution of primitive rational points and of primitive rational points defined by monomials along long horocycle orbits in products of the torus and the modular surface. This answers a question posed in joint wor…
View article: Simultaneous supersingular reductions of CM elliptic curves
Simultaneous supersingular reductions of CM elliptic curves Open
We study the simultaneous reductions at several supersingular primes of elliptic curves with complex multiplication. We show -- under additional congruence assumptions on the CM order -- that the reductions are surjective (and even become …
View article: Primitive rational points on expanding horospheres in Hilbert modular\n surfaces
Primitive rational points on expanding horospheres in Hilbert modular\n surfaces Open
In recent work by Einsiedler, Mozes, Shah and Shapira the limiting\ndistributions of primitive rational points on expanding horospheres was\nexamined in arbitrary dimension, and a suspended version of this result was\nannounced. Motivated …