Publications (31)
Selective orders in central simple algebras and isospectral families of arithmetic manifolds
Benjamin Linowitz
Let be a number field and be a central simple algebra over of dimension where is prime. In the case that we assume that is not totally definite. In…
The spectral geometry of hyperbolic and spherical manifolds: analogies and open problems
Emilio A. Lauret, Benjamin Linowitz
The spectral geometry of negatively curved manifolds has received more attention than its positive curvature counterpart. In this paper we will survey a variety of spectral geometr…
Isospectral towers of Riemannian Manifolds
Benjamin Linowitz
In this paper we construct, for n >= 2, arbitrarily large families of infinite towers of compact, orientable Riemannian n-manifolds which are isospectral but not isometric at each…
Brauer equivalent number fields and the geometry of quaternionic Shimura varieties
Benjamin Linowitz
Two number fields are said to be Brauer equivalent if there is an isomorphism between their Brauer groups that commutes with restriction. In this paper we prove a variety of number…
Commensurability Classes of Fake Quadrics
Benjamin Linowitz, Matthew Stover, John Voight
A fake quadric is a smooth projective surface that has the same rational cohomology as a smooth quadric surface but is not biholomorphic to one. We provide an explicit classificati…
On the isospectral orbifold-manifold problem for nonpositively curved locally symmetric spaces
Benjamin Linowitz, Jeffrey S. Meyer
An old problem asks whether a Riemannian manifold can be isospectral to a Riemannian orbifold with nontrivial singular set. In this short note we show that under the assumption of…
Constructing multi-cusped hyperbolic manifolds that are isospectral and not isometric
Benjamin Linowitz
In a recent paper Garoufalidis and Reid constructed pairs of 1-cusped hyperbolic 3-manifolds which are isospectral but not isometric. In this paper we extend this work to the multi…
Parametrizing Shimura subvarieties of Shimura varieties and related geometric problems
Benjamin Linowitz, Matthew Stover
This paper gives a complete parametrization of the commensurability classes of totally geodesic subspaces of irreducible arithmetic quotients of $X_{a, b} = (\mathbf{H}^2)^a \times…
Local Selectivity of Orders in Central Simple Algebras
Benjamin Linowitz, Thomas R. Shemanske
Let be a central simple algebra of degree over a number field , and a strictly maximal subfield. We say that the ring of integers is "selecti…
The sign changes of Fourier coefficients of Eisenstein series
Benjamin Linowitz, Lola Thompson
In this paper we prove a number of theorems that determine the extent to which the signs of the Hecke eigenvalues of an Eisenstein newform determine the newform. We address this pr…
A non-commutative analogue of the Odlyzko bounds and bounds on performance for space-time lattice codes
Benjamin Linowitz, Matthew Satriano, Roope Vehkalahti
This paper considers space-time coding over several independently Rayleigh faded blocks. In particular we will concentrate on giving upper bounds for the coding gain of lattice spa…
Systole inequalities for arithmetic locally symmetric spaces
Sara Lapan, Benjamin Linowitz, Jeffrey S. Meyer
In this paper we study the systole growth of arithmetic locally symmetric spaces up congruence covers and show that this growth is at least logarithmic in volume. This generalizes…
Universal systole bounds for arithmetic locally symmetric spaces
Sara Lapan, Benjamin Linowitz, Jeffrey S. Meyer
The systole of a closed Riemannian manifold is the minimal length of a non-contractible closed loop. We give a uniform lower bound for the systole for large classes of simple arith…
Locally Equivalent Correspondences
Benjamin Linowitz, D. B. McReynolds, Nicholas Miller
Given a pair of number fields with isomorphic rings of adeles, we construct bijections between objects associated to the pair. For instance we construct an isomorphism of Brauer gr…
Counting problems for geodesics on arithmetic hyperbolic surfaces
Benjamin Linowitz
It is a longstanding problem to determine the precise relationship between the geodesic length spectrum of a hyperbolic manifold and its commensurability class. A well known result…
Systoles of Arithmetic Hyperbolic 2- and 3-Manifolds
Laurel Heck, Benjamin Linowitz
In this paper we study the systoles of arithmetic hyperbolic 2- and 3-manifolds. Our first result is the construction of infinitely many arithmetic hyperbolic 2- and 3-manifolds wh…
Characterizing Hilbert modular cusp forms by coefficient size
Benjamin Linowitz
Associated to an (adelic) Hilbert modular form is a sequence of `Fourier coefficients' which uniquely determine the form. In this paper we characterize Hilbert modular cusp forms b…
Embedding Orders Into Central Simple Algebras
Benjamin Linowitz, Thomas R. Shemanske
The question of embedding fields into central simple algebras over a number field was the realm of class field theory. The subject of embedding orders contained in the ring…
On fields of definition of arithmetic Kleinian reflection groups II
Mikhail Belolipetsky, Benjamin Linowitz
Following the previous work of Nikulin and Agol, Belolipetsky, Storm, and Whyte it is known that there exist only finitely many (totally real) number fields that can serve as field…
Small isospectral and nonisometric orbifolds of dimension 2 and 3
Benjamin Linowitz, John Voight
Revisiting a construction due to Vigneras, we exhibit small pairs of orbifolds and manifolds of dimension 2 and 3 arising from arithmetic Fuchsian and Kleinian groups that are Lapl…
Modular forms on noncongruence subgroups and Atkin-Swinnerton-Dyer relations
Liqun Fang, J. William Hoffman, Benjamin Linowitz +2
We give new examples of weight three cusp forms on noncongruence subgroups of SL(2, Z) whose Scholl representation is modular and which satisfy three term Atkin-Swinnerton-Dyer rel…
Counting and effective rigidity in algebra and geometry
Benjamin Linowitz, D. B. McReynolds, Paul Pollack +1
The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic…
Families of mutually isospectral Riemannian orbifolds
Benjamin Linowitz
In this paper we consider three arithmetic families of isospectral non-isometric Riemannian orbifolds and in each case derive an upper bound for the size of the family which is pol…
Decomposition theorems for Hilbert modular newforms
Benjamin Linowitz
Let $\mathscr{S}_k^+(\cn,Φ)$ denote the space generated by Hilbert modular newforms (over a fixed totally real field ) of weight , level $\cn$ and Hecke character . We s…
Areas of totally geodesic surfaces of hyperbolic 3-orbifolds
Benjamin Linowitz, D. B. McReynolds, Nicholas Miller
The geodesic length spectrum of a complete, finite volume, hyperbolic 3-orbifold M is a fundamental invariant of the topology of M via Mostow-Prasad Rigidity. Motivated by this, th…
Counting isospectral manifolds
Mikhail Belolipetsky, Benjamin Linowitz
Given a simple Lie group of real rank at least we show that the maximum cardinality of a set of isospectral non-isometric -locally symmetric spaces of volume at most …
Systolic Surfaces of Arithmetic Hyperbolic 3-Manifolds
Benjamin Linowitz, Jeffrey S. Meyer
In this paper we examine the geometry of minimal surfaces of arithmetic hyperbolic 3-manifolds. In particular, we give bounds on the totally geodesic 2-systole, construct infinitel…
Selectivity in Quaternion Algebras
Benjamin Linowitz
We prove an integral version of the classical Albert-Brauer-Hasse-Noether theorem regarding quaternion algebras over number fields. Let be a quaternion algebra over a…
The length spectra of arithmetic hyperbolic 3-manifolds and their totally geodesic surfaces
Benjamin Linowitz, Jeffrey S. Meyer, Paul Pollack
In this paper we examine the relationship between the length spectrum and the geometric genus spectrum of an arithmetic hyperbolic 3-orbifold M. In particular we analyze the extent…
Systoles of Arithmetic Hyperbolic Surfaces and 3-manifolds
Benjamin Linowitz, D. B. McReynolds, Paul Pollack +1
Our main result is that for all sufficiently large , the set of commensurability classes of arithmetic hyperbolic 2- or 3-orbifolds with fixed invariant trace field and…
Bounded gaps between primes and the length spectra of arithmetic hyperbolic 3-orbifolds
Benjamin Linowitz, D. B. McReynolds, Paul Pollack +1
In 1992, Reid asked whether hyperbolic 3-manifolds with the same geodesic length spectra are necessarily commensurable. While this is known to be true for arithmetic hyperbolic 3-m…