Uri Shapira

activity

20082025

most citedInteger points and their orthogonal lattices

16 citations · 83 across the 21 of their papers we have counts for

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9 papers · 1 filter

math.NT2025

Escape of mass of the Thue-Morse sequence

Erez Nesharim, Uri Shapira, Noy Soffer Aranov

Every Laurent series in $F_{q} ((t^{- 1}))$ has a continued fraction expansion whose partial quotients are polynomials. De Mathan and Teulié proved that…

math.NT2022

Geometric and arithmetic aspects of approximation vectors

Uri Shapira, Barak Weiss

Let $θ \in R^{d}$ . We associate three objects to each approximation $(p, q) \in Z^{d} \times N$ of $θ$ : the projection of the lattice $Z^{d + 1}$ to the hy…

math.NT2021

Linnik's problem in fiber bundles over quadratic homogeneous varieties

Michael Bersudsky, Uri Shapira

We compute the statistics of $S L_{d} (Z)$ matrices lying on level sets of an integral polynomial defined on $S L_{d} (R)$ , a result that is a variant of the well kno…

math.NT2016

Shapes of unit lattices and escape of mass

Ofir David, Uri Shapira

We study the collection of points on the modular surface obtained from the logarithm embeddings of the groups of units in totally real cubic number fields. We conjecture that this…

math.NT2016★ 8 cited

Counterexamples to a conjecture of Woods

Oded Regev, Uri Shapira, Barak Weiss

A conjecture of Woods from 1972 is disproved.

math.NT2015★ 16 cited

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…

math.NT2014★ 12 cited

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…

math.NT2014

A volume estimate for the set of stable lattices

Uri Shapira, Barak Weiss

We show that in high dimensions the set of stable lattices is almost of full measure in the space of unimodular lattices.

math.NT2012

Remarks on Euclidean Minima

Uri Shapira, Zhiren Wang

The Euclidean minimum $M (K)$ of a number field $K$ is an important numerical invariant that indicates whether $K$ is norm-Euclidean. When $K$ is a non-CM field of unit rank 2 or hi…