16 citations · 48 across the 14 of their papers we have counts for
20 papers
The Fully Inhomogeneous -Adic Littlewood Conjecture
Menny Aka, Alexander Gorodnik, Pankaj Vishe +1
We prove that for almost every , the \textit{fully inhomogeneous -adic Littlewood Conjecture} holds; namely, $$\forall\, δ\in\mathbb{R},\;\forall\, κ\in\mathbb{Z…
Planes in quadratic 4-space and associated shapes of lattices
Menny Aka, Konstantin Andritsch, Andreas Wieser
Let be the standard signature quadratic form. To each non-degenerate rational plane in the four-dimensional quadratic space $(\mathbb{Q}^4,…
Fibonacci sequences in
Menny Aka
We prove a conjecture due to Gica (Fibonacci Quarterly, 2008). Our proof is simple, uses only elementary abstract algebra, and generalizes to other recursive sequences.
Seifert surfaces in the four-ball and composition of binary quadratic forms
Menny Aka, Peter Feller, Alison Beth Miller +1
We use composition of binary quadratic forms to systematically create pairs of Seifert surfaces that are non-isotopic in the four-ball. Our main topological result employs Gauss co…
Joinings classification and applications [after Einsiedler and Lindenstruass]
Menny Aka
This is the text accompanying my Bourbaki seminar on the work of Einsiedler and Lindenstrauss on joinings. The first five sections surveys their proof of the classification of join…
Equidistribution of rational subspaces and their shapes
Menny Aka, Andrea Musso, Andreas Wieser
To any -dimensional subspace of one can naturally associate a point in the Grassmannian and two shapes of lattices of rank and $n-k…
Simultaneous supersingular reductions of CM elliptic curves
Menny Aka, Manuel Luethi, Philippe Michel +1
We study the simultaneous reductions at several supersingular primes of elliptic curves with complex multiplication. We show -- under additional congruence assumptions on the CM or…
Planes in four space and four associated CM points
Menny Aka, Manfred Einsiedler, Andreas Wieser
To any two-dimensional rational plane in four-dimensional space one can naturally attach a point in the Grassmannian Gr(2,4) and four lattices of rank two. Here, the first two latt…
Continued Fractions of Arithmetic Sequences of Quadratics
Menny Aka
Let x be a quadratic irrational and let P be the set of prime numbers. We show the existence of an infinite subset S of P such that the statistics of the period of the continued fr…
On effective equidistribution for quotients of SL(d)
Menny Aka, Manfred Einsiedler, Han Li +1
We prove the first case of polynomially effective equidistribution of closed orbits of semisimple groups with nontrivial centralizer. The proof relies on uniform spectral gap, buil…
Diophantine approximation on matrices and Lie groups
Menny Aka, Emmanuel Breuillard, Lior Rosenzweig +1
We study the general problem of extremality for metric Diophantine approximation on submanifolds of matrices. We formulate a criterion for extremality in terms of a certain family…
Integer points and their orthogonal lattices
Menny Aka, Manfred Einsiedler, Uri Shapira
Linnik proved in the late 1950's the equidistribution of integer points on large spheres under a congruence condition. The congruence condition was lifted in 1988 by Duke (building…
Integer points on spheres and their orthogonal grids
Menny Aka, Manfred Einsiedler, Uri Shapira
The set of primitive vectors on large spheres in the euclidean space of dimension d>2 equidistribute when projected on the unit sphere. We consider here a refinement of this proble…
On metric diophantine approximation in matrices and Lie groups
Menny Aka, Emmanuel Breuillard, Lior Rosenzweig +1
We study the diophantine exponent of analytic submanifolds of the space of m by n real matrices, answering questions of Beresnevich, Kleinbock and Margulis. We identify a family of…
Duke's Theorem for subcollections
Menny Aka, Manfred Einsiedler
We combine effective mixing and Duke's Theorem on closed geodesics on the modular surface to show that certain subcollections of the collection of geodesics with a given discrimina…
Diophantine properties of nilpotent Lie groups
Menny Aka, Emmanuel Breuillard, Lior Rosenzweig +1
A finitely generated subgroup Γ of a real Lie group G is said to be Diophantine if there is β> 0 such that non-trivial elements in the word ball B_Γ(n) centered at the identity nev…
Homogeneous number of free generators
Menny Aka, Tsachik Gelander, Gregory A. Soifer
We address two questions of Simon Thomas. First, we show that for any n>2 one can find a four generated free subgroup of SLn(Z) which is profinitely dense. More generally, we show…
On the evolution of continued fractions in a fixed quadratic field
Menny Aka, Uri Shapira
We prove that the statistics of the period of the continued fraction expansion of certain sequences of quadratic irrationals from a fixed quadratic field approach the `normal' stat…
Arithmetic groups with isomorphic finite quotients
Menny Aka
Two finitely generated groups have the same set of finite quotients if and only if their profinite completions are isomorphic. Consider the map which sends (the isomorphism class o…
Profinite completions and Kazhdan's property (T)
Menny Aka
We show that property (T) is not profinite, that is, we construct two finitely generated residually finite groups which have isomorphic profinite completions while one admits prope…