Project MUSE®: American Journal of Mathematics - Latest Articles
https://muse.jhu.edu/journals/american_journal_of_mathematics
Project MUSE®: Latest articles in American Journal of Mathematics.daily12015-09-01T04:00:33-05:00text/htmlen-USThe Johns Hopkins University PressVol. 118 (1996) through current issueLatest Articles: American Journal of MathematicsMathematicsTWOProject MUSE®American Journal of Mathematics1080-63770002-9327Latest articles in American Journal of Mathematics. Feed provided by Project MUSE®The semiclassical theory of discontinuous systems and ray-splitting billiards
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.4.jakobson.html
<p>By Dmitry Jakobson, Yuri Safarov, Alexander Strohmaier, Alexander Yves Colin De Verdière</p>
We analyze the semiclassical limit of spectral theory on manifolds whose metrics have jump-like discontinuities. Such systems are quite different from manifolds with smooth Riemannian metrics because the semiclassical limit does not relate to a classical flow but rather to branching (ray-splitting) billiard dynamics. In order to describe this system we introduce a dynamical system on the space of functions on phase space. To identify the quantum dynamics in the semiclassical limit we compute the principal symbols of the Fourier integral operators associated to reflected and refracted geodesic rays and identify the relation between classical and quantum dynamics. In particular we prove a quantum ergodicity theorem ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.4.jakobson.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-09-01T04:00:33-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgThe semiclassical theory of discontinuous systems and ray-splitting billiards2015-07-10text/htmlen-USThe Johns Hopkins University PressThe semiclassical theory of discontinuous systems and ray-splitting billiards2015-07-102015TWOProject MUSE®02015-07-10T00:00:00-05:002015-07-10On the images and poles of degenerate Eisenstein series for ${\rm GL}(n,\Bbb{A}_{\Bbb{Q}})$ and ${\rm GL}(n,\Bbb{R})$
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.4.hanzer.html
<p>By Marcela Hanzer, Goran Muić</p>
In this paper we determine poles in the right-half plane and images of degenerate Eisenstein series for ${\rm GL}_n(\Bbb{A}_{\Bbb{Q}})$ induced from a character on a maximal parabolic subgroup. We apply those results to determine poles of degenerate Eisenstein series for ${\rm ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.4.hanzer.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-09-01T04:00:33-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgOn the images and poles of degenerate Eisenstein series for ${\rm GL}(n,\Bbb{A}_{\Bbb{Q}})$ and ${\rm GL}(n,\Bbb{R})$2015-07-10text/htmlen-USThe Johns Hopkins University PressOn the images and poles of degenerate Eisenstein series for ${\rm GL}(n,\Bbb{A}_{\Bbb{Q}})$ and ${\rm GL}(n,\Bbb{R})$2015-07-102015TWOProject MUSE®02015-07-10T00:00:00-05:002015-07-10Eisenstein series on covers of odd orthogonal groups
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.4.friedberg.html
<p>By Solomon Friedberg, Lei Zhang</p>
We study the Whittaker coefficients of the minimal parabolic Eisenstein series on the n-fold cover of the split odd orthogonal group SO2r+1. If the degree of the cover is odd, then Beineke, Brubaker and Frechette have conjectured that the p-power contributions to the Whittaker coefficients may be computed using the theory of crystal graphs of type C, by attaching to each path component a Gauss sum or a degenerate Gauss sum depending on the fine structure of the path. We establish their conjecture using a combination of automorphic and combinatorial-representation-theoretic methods. Surprisingly, we must make use of the type A theory, and the two different crystal graph descriptions of Brubaker, Bump and Friedberg ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.4.friedberg.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-09-01T04:00:33-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgEisenstein series on covers of odd orthogonal groups2015-07-10text/htmlen-USThe Johns Hopkins University PressEisenstein series on covers of odd orthogonal groups2015-07-102015TWOProject MUSE®02015-07-10T00:00:00-05:002015-07-10Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.4.cantat.html
<p>By Serge Cantat, Keiji Oguiso</p>
Thanks to the theory of Coxeter groups, we produce the first family of Calabi-Yau manifolds X of arbitrary dimension n, for which Bir(X) is infinite and the Kawamata-Morrison movable cone conjecture is satisfied. For this family, the movable cone is explicitly described; it’s fractal nature is related to limit sets of Kleinian groups and to the Apollonian Gasket. Then, we produce explicit examples of (biregular) automorphisms with positive entropy on some Calabi-Yau ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.4.cantat.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-09-01T04:00:33-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgBirational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups2015-07-10text/htmlen-USThe Johns Hopkins University PressBirational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups2015-07-102015TWOProject MUSE®02015-07-10T00:00:00-05:002015-07-10Multi-marginal optimal transport on Riemannian manifolds
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.4.kim.html
<p>By Young-Heon Kim, Brendan Pass</p>
We study a multi-marginal optimal transportation problem on a Riemannian manifold, with cost function given by the average distance squared from multiple points to their barycenter. Under a standard regularity condition on the first marginal, we prove that the optimal measure is unique and concentrated on the graph of a function over the first variable, thus inducing a Monge solution. This result generalizes McCann’s polar factorization theorem on manifolds from two to several marginals, in the same sense that a well-known result of Gangbo and Swiech generalizes Brenier’s polar factorization theorem on ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.4.kim.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-09-01T04:00:33-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgMulti-marginal optimal transport on Riemannian manifolds2015-07-10text/htmlen-USThe Johns Hopkins University PressMulti-marginal optimal transport on Riemannian manifolds2015-07-102015TWOProject MUSE®02015-07-10T00:00:00-05:002015-07-10Fourier coefficients of harmonic weak Maass forms and the partition function
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.4.masri.html
<p>By Riad Masri</p>
In a recent paper, Bruinier and Ono proved that certain harmonic weak Maass forms have the property that the Fourier coefficients of their holomorphic parts are algebraic traces of weak Maass forms evaluated on Heegner points. As a special case they obtained a remarkable finite algebraic formula for the Hardy-Ramanujan partition function p(n), which counts the number of partitions of a positive integer n. We establish an asymptotic formula with a power saving error term for the Fourier coefficients in the Bruinier-Ono formula. As a consequence, we obtain a new asymptotic formula for p(n). One interesting feature of this formula is that the main term contains essentially 3 ·h(−24n+1) fewer terms than the truncated ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.4.masri.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-09-01T04:00:33-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgFourier coefficients of harmonic weak Maass forms and the partition function2015-07-10text/htmlen-USThe Johns Hopkins University PressFourier coefficients of harmonic weak Maass forms and the partition function2015-07-102015TWOProject MUSE®02015-07-10T00:00:00-05:002015-07-10On the restriction of Zuckerman’s derived functor modules Aq(λ) to reductive subgroups
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.4.oshima.html
<p>By Yoshiki Oshima</p>
In this article, we study the restriction of Zuckerman’s derived functor (g, K)-modules Aq(λ) to g′ for symmetric pairs of reductive Lie algebras (g, g′). When the restriction decomposes into irreducible (g′, K′)-modules, we give an upper bound for the branching law. In particular, we prove that each (g′, K′)-module occurring in the restriction is isomorphic to a submodule of Aq′ (λ′) for a parabolic subalgebra q′ of g′, and determine their associated varieties. For the proof, we realize Aq(λ) on complex partial flag varieties by using ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.4.oshima.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-09-01T04:00:33-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgOn the restriction of Zuckerman’s derived functor modules Aq(λ) to reductive subgroups2015-07-10text/htmlen-USThe Johns Hopkins University PressOn the restriction of Zuckerman’s derived functor modules Aq(λ) to reductive subgroups2015-07-102015TWOProject MUSE®02015-07-10T00:00:00-05:002015-07-10A short proof of the multidimensional Szemerédi theorem in the primes
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.4.fox.html
<p>By Jacob Fox, Yufei Zhao</p>
Tao conjectured that every dense subset of Pd, the d-tuples of primes, contains constellations of any given shape. This was very recently proved by Cook, Magyar, and Titichetrakun and independently by Tao and Ziegler. Here we give a simple proof using the Green-Tao theorem on linear equations in primes and the Furstenberg-Katznelson multidimensional Szemerédi ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.4.fox.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-09-01T04:00:33-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgA short proof of the multidimensional Szemerédi theorem in the primes2015-07-10text/htmlen-USThe Johns Hopkins University PressA short proof of the multidimensional Szemerédi theorem in the primes2015-07-102015TWOProject MUSE®02015-07-10T00:00:00-05:002015-07-10Semiclassical completely integrable systems: long-time dynamics and observability via two-microlocal Wigner measures
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.3.anantharaman.html
<p>By Nalini Anantharaman, Clotilde Fermanian-Kammerer, Fabricio Macià</p>
We look at the long-time behavior of solutions to a semi-classical Schr\"odinger equation on the torus. We consider time scales which go to infinity when the semi-classical parameter goes to zero and we associate with each time-scale the set of semi-classical measures associated with all possible choices of initial data. On each classical invariant torus, the structure of semi-classical measures is described in terms of two-microlocal measures, obeying explicit propagation laws. We apply this construction in two directions. We first analyze the regularity of semi-classical measures, and we emphasize the existence of a threshold: for time-scales below this threshold, the set of semi-classical measures contains ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.3.anantharaman.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-09-01T04:00:33-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgSemiclassical completely integrable systems: long-time dynamics and observability via two-microlocal Wigner measures2015-05-28text/htmlen-USThe Johns Hopkins University PressSemiclassical completely integrable systems: long-time dynamics and observability via two-microlocal Wigner measures2015-05-282015TWOProject MUSE®02015-05-28T00:00:00-05:002015-05-28Complex multiplication cycles and Kudla-Rapoport divisors, II
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.3.howard.html
<p>By Benjamin Howard</p>
This paper is about the arithmetic of {\it Kudla-Rapoport divisors} on Shimura varieties of type ${\rm GU}(n-1,1)$. In the first part of the paper we construct a toroidal compactification of N.~Kr\"amer's integral model of the Shimura variety. This extends work of K.-W.~Lan, who constructed a compactification at unramified primes. In the second, and main, part of the paper we use ideas of Kudla to construct Green functions for the Kudla-Rapoport divisors on the open Shimura variety, and analyze the behavior of these functions near the boundary of the compactification. The Green functions turn out to have logarithmic singularities along certain components of the boundary, up to log-log error terms. Thus, by ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.3.howard.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-09-01T04:00:33-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgComplex multiplication cycles and Kudla-Rapoport divisors, II2015-05-28text/htmlen-USThe Johns Hopkins University PressComplex multiplication cycles and Kudla-Rapoport divisors, II2015-05-282015TWOProject MUSE®02015-05-28T00:00:00-05:002015-05-28