Project MUSE®: American Journal of Mathematics - Latest Articles
http://muse.jhu.edu/journal/5
Project MUSE®: Latest articles in Africa Today.daily12016-08-26T00:00:00-05:00text/htmlen-USThe Johns Hopkins University PressVol. 118 (1996) through current issueLatest Articles: American Journal of MathematicsTWOProject MUSE®American Journal of Mathematics1080-63770002-9327Latest articles in American Journal of Mathematics. Feed provided by Project MUSE®Affine Grassmannians of group schemes and exotic principal bundles over ${\Bbb A}^1$
http://muse.jhu.edu/article/628315
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Let G be a simple simply-connected group scheme over a regular local scheme U. Let ε be a principal G-bundle over trivial away from a subscheme finite over U. We show that ε is not necessarily trivial and give some criteria of triviality. To this end, we define affine Grassmannians for group schemes and study their Bruhat decompositions for semi-simple group schemes. We also give examples of principal G-bundles over with split G such that the bundles are not isomorphic to pullbacks from
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Project MUSE®http://muse.jhu.edu/2016-08-26T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallAffine Grassmannians of group schemes and exotic principal bundles over ${\Bbb A}^1$2016-08-10text/htmlen-USThe Johns Hopkins University PressAffine Grassmannians of group schemes and exotic principal bundles over ${\Bbb A}^1$2016-08-102016TWOProject MUSE®322772016-08-26T00:00:00-05:002016-08-10Uniform estimates for bilinear Hilbert transforms and bilinear maximal functions associated to polynomials
http://muse.jhu.edu/article/628316
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We study the bilinear Hilbert transforms and bilinear maximal functions associated to non-flat polynomial curves and obtain uniform Lr estimates for r>d−1d, where d is the degree of the polynomial. In addition, the lower bound of r is sharp up to the end
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Project MUSE®http://muse.jhu.edu/2016-08-26T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallUniform estimates for bilinear Hilbert transforms and bilinear maximal functions associated to polynomials2016-08-10text/htmlen-USThe Johns Hopkins University PressUniform estimates for bilinear Hilbert transforms and bilinear maximal functions associated to polynomials2016-08-102016TWOProject MUSE®265062016-08-26T00:00:00-05:002016-08-10Generic vanishing in characteristic p > 0 and the characterization of ordinary abelian varieties
http://muse.jhu.edu/article/628317
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We prove a generic vanishing type statement in positive characteristic and apply it to prove positive characteristic versions of Kawamata’s theorems: a characterization of smooth varieties birational to ordinary abelian varieties and the surjectivity of the Albanese map when the Frobenius stable Kodaira dimension is
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Project MUSE®http://muse.jhu.edu/2016-08-26T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallGeneric vanishing in characteristic p > 0 and the characterization of ordinary abelian varieties2016-08-10text/htmlen-USThe Johns Hopkins University PressGeneric vanishing in characteristic p > 0 and the characterization of ordinary abelian varieties2016-08-102016TWOProject MUSE®404572016-08-26T00:00:00-05:002016-08-10The sup-norm problem on the Siegel modular space of rank two
http://muse.jhu.edu/article/628318
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Let F be a square integrable Maaß form on the Siegel upper half space ℌ of rank 2 for the Siegel modular group Sp4(ℤ) with Laplace eigenvalue λ. If, in addition, F is a joint eigenfunction of the Hecke algebra and Ω is a compact set in Sp4(ℤ)\ℌ, we show the bound ||F|Ω||∞ ≪ Ω (1 + λ)1−δ for some global constant δ > 0. As an auxiliary result of independent interest we prove new uniform bounds for spherical functions on semisimple Lie
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Project MUSE®http://muse.jhu.edu/2016-08-26T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallThe sup-norm problem on the Siegel modular space of rank two2016-08-10text/htmlen-USThe Johns Hopkins University PressThe sup-norm problem on the Siegel modular space of rank two2016-08-102016TWOProject MUSE®385492016-08-26T00:00:00-05:002016-08-10Polynomials vanishing on grids: The Elekes-Rónyai problem revisited
http://muse.jhu.edu/article/628319
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In this paper we characterize real bivariate polynomials which have a small range over large Cartesian products. We show that for every constant-degree bivariate real polynomial f, either |f(A, B)| = Ω(n4/3), for every pair of finite sets A, B ⊂ ℝ, with |A| = |B| = n (where the constant of proportionality depends on deg f), or else f must be of one of the special forms f(u, v) = h (φ(u) + ψ(v)), or f(u, v) = h(φ(u) · ψ(v)), for some univariate polynomials φ, ψ, h over ℝ. This significantly improves a result of Elekes and Rónyai (2000). Our results are cast in a more general form, in which we give an upper bound for the number of zeros of z = f(x, y) on a triple Cartesian product A × B × C, when the sizes |A|, |B|
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Project MUSE®http://muse.jhu.edu/2016-08-26T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallPolynomials vanishing on grids: The Elekes-Rónyai problem revisited2016-08-10text/htmlen-USThe Johns Hopkins University PressPolynomials vanishing on grids: The Elekes-Rónyai problem revisited2016-08-102016TWOProject MUSE®390452016-08-26T00:00:00-05:002016-08-10Renormalized Chern-Gauss-Bonnet formula for complete Kähler-Einstein metrics
http://muse.jhu.edu/article/628320
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We present a renormalized Gauss-Bonnet formula for a strictly pseudoconvex manifold with a complete Kähler metric given by a globally defined potential function near the boundary. When the metric is asymptotically Einstein, the boundary contribution in the formula is explicitly written down in terms of the pseudo-hermitian geometry of the boundary and is shown to be a global CR invariant. The CR invariant generalizes the Burns-Epstein invariant on 3-dimensional CR
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Project MUSE®http://muse.jhu.edu/2016-08-26T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallRenormalized Chern-Gauss-Bonnet formula for complete Kähler-Einstein metrics2016-08-10text/htmlen-USThe Johns Hopkins University PressRenormalized Chern-Gauss-Bonnet formula for complete Kähler-Einstein metrics2016-08-102016TWOProject MUSE®262292016-08-26T00:00:00-05:002016-08-10Flowing maps to minimal surfaces
http://muse.jhu.edu/article/628321
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We introduce a flow of maps from a compact surface of arbitrary genus to an arbitrary Riemannian manifold which has elements in common with both the harmonic map flow and the mean curvature flow, but is more effective at finding minimal surfaces. In the genus 0 case, our flow is just the harmonic map flow, and it tries to find branched minimal 2-spheres as in Sacks-Uhlenbeck (1981) and Struwe (1985), etc. In the genus 1 case, we show that our flow is exactly equivalent to that considered by Ding-Li-Liu (2006). In general, we recover the result of Schoen-Yau (1979) and Sacks-Uhlenbeck (1982) that an incompressible map from a surface can be adjusted to a branched minimal immersion with the same action on π1, and this
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Project MUSE®http://muse.jhu.edu/2016-08-26T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallFlowing maps to minimal surfaces2016-08-10text/htmlen-USThe Johns Hopkins University PressFlowing maps to minimal surfaces2016-08-102016TWOProject MUSE®182072016-08-26T00:00:00-05:002016-08-10On special values of certain L-functions, II
http://muse.jhu.edu/article/628322
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We prove an algebraicity result concerning special values at critical points, in the sense of Deligne, of tensor product L-functions associated to automorphic representations of special orthogonal groups for quadratic forms which are totally definite, and, cuspidal representations of GL(2) corresponding to primitive cusp forms, over totally real number fields. We also prove the reciprocity law, i.e., the equivariance under the action of Gal(/ℚ), for the special values. In the appendix, the second author calculates the Deligne periods for such L-functions, assuming the existence of corresponding motives and the automorphic transfer to a quasi-split form of the special orthogonal group. Our result conforms with the
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Project MUSE®http://muse.jhu.edu/2016-08-26T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallOn special values of certain L-functions, II2016-08-10text/htmlen-USThe Johns Hopkins University PressOn special values of certain L-functions, II2016-08-102016TWOProject MUSE®434262016-08-26T00:00:00-05:002016-08-10