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.daily12015-04-18T04:00:39-05:00text/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 Tate Conjecture for a family of surfaces of general type with pg = q = 1 and K2 = 3
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.lyons.html
<p>By Christopher Lyons</p>
We prove a big monodromy result for a smooth family of complex algebraic surfaces of general type, with invariants pg = q = 1 and K2 = 3, that has been introduced by Catanese and Ciliberto. This is accomplished via a careful study of degenerations. As corollaries, when a surface in this family is defined over a finitely generated extension of ℚ, we verify the semisimplicity and Tate conjectures for the Galois representation on the middle ℓ-adic cohomology of the ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.lyons.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-04-18T04:00:39-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgThe Tate Conjecture for a family of surfaces of general type with pg = q = 1 and K2 = 32015-04-13text/htmlen-USThe Johns Hopkins University PressThe Tate Conjecture for a family of surfaces of general type with pg = q = 1 and K2 = 32015-04-132015TWOProject MUSE®02015-04-13T00:00:00-05:002015-04-13On the boundedness of the bilinear Hilbert transform along “non-flat” smooth curves
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.lie.html
<p>By Victor Lie</p>
We are proving L2(ℝ) × L2(ℝ) → L1(ℝ) bounds for the bilinear Hilbert transform HΓ along curves Γ = (t,−γ(t)) with γ being a smooth “non-flat” curve near zero and ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.lie.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-04-18T04:00:39-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgOn the boundedness of the bilinear Hilbert transform along “non-flat” smooth curves2015-04-13text/htmlen-USThe Johns Hopkins University PressOn the boundedness of the bilinear Hilbert transform along “non-flat” smooth curves2015-04-132015TWOProject MUSE®02015-04-13T00:00:00-05:002015-04-13Confluent A-hypergeometric functions and rapid decay homology cycles
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.esterov.html
<p>By Alexander Esterov, Kiyoshi Takeuchi</p>
We study confluent A-hypergeometric functions introduced by Adolphson. In particular, we give their integral representations by using rapid decay homology cycles of Hien. The method of toric compactifications introduced in our previous works will be used to prove our main theorem. Moreover we apply it to obtain a formula for the asymptotic expansions at infinity of confluent A-hypergeometric ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.esterov.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-04-18T04:00:39-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgConfluent A-hypergeometric functions and rapid decay homology cycles2015-04-13text/htmlen-USThe Johns Hopkins University PressConfluent A-hypergeometric functions and rapid decay homology cycles2015-04-132015TWOProject MUSE®02015-04-13T00:00:00-05:002015-04-13The expected total curvature of random polygons
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.cantarella.html
<p>By Jason Cantarella, Alexander Y. Grosberg, Robert Kusner, Clayton Shonkwiler</p>
We consider the expected value for the total curvature of a random closed polygon. Numerical experiments have suggested that as the number of edges becomes large, the difference between the expected total curvature of a random closed polygon and a random open polygon with the same number of turning angles approaches a positive constant. We show that this is true for a natural class of probability measures on polygons, and give a formula for the constant in terms of the moments of the edgelength distribution. We then consider the symmetric measure on closed polygons of fixed total length constructed by Cantarella, Deguchi, and Shonkwiler. For this measure, we are able to prove that the expected value of total ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.cantarella.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-04-18T04:00:39-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgThe expected total curvature of random polygons2015-04-13text/htmlen-USThe Johns Hopkins University PressThe expected total curvature of random polygons2015-04-132015TWOProject MUSE®02015-04-13T00:00:00-05:002015-04-13Degenerate Whittaker functionals for real reductive groups
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.gourevitch.html
<p>By Dmitry Gourevitch, Siddhartha Sahi</p>
In this paper we establish a connection between the associated variety of a representation and the existence of certain degenerate Whittaker functionals, for both smooth and K-finite vectors, for all quasi-split real reductive groups, thereby generalizing results of Kostant, Matumoto and ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.gourevitch.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-04-18T04:00:39-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgDegenerate Whittaker functionals for real reductive groups2015-04-13text/htmlen-USThe Johns Hopkins University PressDegenerate Whittaker functionals for real reductive groups2015-04-132015TWOProject MUSE®02015-04-13T00:00:00-05:002015-04-13The LS method for the classical groups in positive characteristic and the Riemann Hypothesis
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.lomeli.html
<p>By Luis Alberto Lomelí</p>
We provide a definition for an extended system of γ-factors for products of generic representations τ and π of split classical groups or general linear groups over a non-archimedean local field of characteristic p. We prove that our γ-factors satisfy a list of axioms (under the assumption p ≠ 2 when both groups are classical groups) and show their uniqueness (in general). This allows us to define extended local L-functions and root numbers. We then obtain automorphic L-functions L(s, τ × π), where τ and π are globally generic cuspidal automorphic representations of split classical groups or general linear groups over a global function field. In addition to rationality and the functional equation, we prove that our ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.lomeli.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-04-18T04:00:39-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgThe LS method for the classical groups in positive characteristic and the Riemann Hypothesis2015-04-13text/htmlen-USThe Johns Hopkins University PressThe LS method for the classical groups in positive characteristic and the Riemann Hypothesis2015-04-132015TWOProject MUSE®02015-04-13T00:00:00-05:002015-04-13An arithmetic intersection formula for denominators of Igusa class polynomials
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.lauter.html
<p>By Kristin Lauter, Bianca Viray</p>
In this paper we prove an explicit formula for the arithmetic intersection number (CM(K). G1)ℓ on the Siegel moduli space of abelian surfaces, generalizing the work of Bruinier-Yang and Yang. These intersection numbers allow one to compute the denominators of Igusa class polynomials, which has important applications to the construction of genus 2 curves for use in cryptography. Bruinier and Yang conjectured a formula for intersection numbers on an arithmetic Hilbert modular surface, and as a consequence obtained a conjectural formula for the intersection number (CM(K). G1)ℓ under strong assumptions on the ramification of the primitive quartic CM field K. Yang later proved this conjecture assuming that OK is freely ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.lauter.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-04-18T04:00:39-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgAn arithmetic intersection formula for denominators of Igusa class polynomials2015-04-13text/htmlen-USThe Johns Hopkins University PressAn arithmetic intersection formula for denominators of Igusa class polynomials2015-04-132015TWOProject MUSE®02015-04-13T00:00:00-05:002015-04-13Time-analyticity of solutions to the Ricci flow
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.kotschwar.html
<p>By Brett Kotschwar</p>
We prove that if g(t) is a smooth, complete solution to the Ricci flow of uniformly bounded curvature on M × [0, Ω], then the correspondence t ↦ g(t) is real-analytic at each t0 ∈ (0, Ω). The analyticity is a consequence of classical Bernstein-type estimates on the temporal and spatial derivatives of the curvature tensor, which we further use to show that, under the above global hypotheses, for any x0 ∈ M and t0 ∈ (0, Ω), there exist local coordinates x = xi on a neighborhood U ⊂ M of x0 in which the representation gij(x,t) of the metric is real-analytic in both x and t on some cylinder U ×(t0 − ϵ,t0 ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.2.kotschwar.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-04-18T04:00:39-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgTime-analyticity of solutions to the Ricci flow2015-04-13text/htmlen-USThe Johns Hopkins University PressTime-analyticity of solutions to the Ricci flow2015-04-132015TWOProject MUSE®02015-04-13T00:00:00-05:002015-04-13On the cohomology groups of local systems over Hilbert modular varieties
via Higgs bundles
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.1.muller-stach.html
<p>By Stefan Müller-Stach, Mao Sheng, Xuanming Ye, Kang Zuo</p>
Let X be a Hilbert modular variety and [inline-graphic 01] a non-trivial local system over X with infinite monodromy. In this paper we study Saito’s mixed Hodge structure (MHS) on the cohomology group Hk (X, [inline-graphic 02]) using the method of Higgs bundles. Among other results we prove the Eichler-Shimura isomorphism, give a dimension formula for the Hodge numbers and show that the mixed Hodge structure is split over ℝ. These results are analogous to the work of Y. Matsushima and G. Shimura in the cocompact case and complement the results of E. Frietag for constant ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.1.muller-stach.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-04-18T04:00:39-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgOn the cohomology groups of local systems over Hilbert modular varieties
via Higgs bundles2015-02-05text/htmlen-USThe Johns Hopkins University PressOn the cohomology groups of local systems over Hilbert modular varieties
via Higgs bundles2015-02-052015TWOProject MUSE®02015-02-05T00:00:00-05:002015-02-05Dirac cohomology of cohomologically induced modules for reductive Lie groups
https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.1.dong.html
<p>By Chao-Ping Dong, Jing-Song Huang</p>
We extend the setting and a proof of the Vogan’s conjecture on Dirac cohomology to a possibly disconnected real reductive Lie group G in the Harish-Chandra class. We show that the Dirac cohomology of cohomologically induced module ℒs (Z) is completely determined by the Dirac cohomology of the inducing module Z. More precisely, we prove that if Z is weakly good then the Dirac cohomology HD(ℒs(Z)) is equal to [inline-graphic 01]. An immediate application is a classification of tempered irreducible unitary representations with nonzero Dirac ... <a href="https://muse.jhu.edu/journals/american_journal_of_mathematics/v137/137.1.dong.html">Read More</a>
Project MUSE®https://muse.jhu.edu/2015-04-18T04:00:39-05:00https://muse.jhu.edu/images/journals/coverImages/ajmcoversmall.jpgDirac cohomology of cohomologically induced modules for reductive Lie groups2015-02-05text/htmlen-USThe Johns Hopkins University PressDirac cohomology of cohomologically induced modules for reductive Lie groups2015-02-052015TWOProject MUSE®02015-02-05T00:00:00-05:002015-02-05