Project MUSE®: American Journal of Mathematics - Latest Articles
http://muse.jhu.edu/journal/5
Project MUSE®: Latest articles in American Journal of Mathematics.daily12017-07-28T00:00:00-05:00text/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®An algebraic study of extension algebras
http://muse.jhu.edu/article/657763
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We present simple conditions which guarantee a geometric extension algebra to behave like a variant of quasi-hereditary algebras. In particular, standard modules of affine Hecke algebras of type BC, and the quiver Schur algebras are shown to satisfy the Brauer-Humphreys type reciprocity and the semi-orthogonality property. In addition, we present a new criterion of purity of weights in the geometric side. This yields a proof of Shoji's conjecture on limit symbols of type B [T. Shoji, Adv. Stud. Pure Math. 40 (2004)], and the purity of the exotic Springer fibers [S. Kato, Duke Math. J. 148 (2009)]. Using this, we describe the leading terms of the C∞-realization of a solution of the Lieb-McGuire system in the
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Project MUSE®http://muse.jhu.edu/2017-07-28T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallAn algebraic study of extension algebras2017-05-03text/htmlen-USThe Johns Hopkins University PressAn algebraic study of extension algebras2017-05-032017TWOProject MUSE®439472017-07-28T00:00:00-05:002017-05-03Lower bounds for resonance counting functions for obstacle scattering in even dimensions
http://muse.jhu.edu/article/657764
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In even dimensional Euclidean scattering, the resonances lie on the logarithmic cover of the complex plane. This paper studies resonances for obstacle scattering in ℝd with Dirichlet, Neumann, or admissible Robin boundary conditions, when d is even. Set nm(r) to be the number of resonances with norm at most r and argument between mπ and (m + 1)π. Then lim if m ∈
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Project MUSE®http://muse.jhu.edu/2017-07-28T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallLower bounds for resonance counting functions for obstacle scattering in even dimensions2017-05-03text/htmlen-USThe Johns Hopkins University PressLower bounds for resonance counting functions for obstacle scattering in even dimensions2017-05-032017TWOProject MUSE®367582017-07-28T00:00:00-05:002017-05-03Special values of adjoint L-functions and congruences for automorphic forms on GL(n) over a number field
http://muse.jhu.edu/article/657765
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We prove an integrality result for the value at s = 1 of the adjoint L-function associated to a cohomological cuspidal automorphic representation on GL(n) over any number field. We then show that primes (outside an exceptional set) dividing this special value give rise to congruences between automorphic forms. We also prove a non-vanishing property at infinity for the relevant Rankin-Selberg L-functions on GL(n) ×
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Project MUSE®http://muse.jhu.edu/2017-07-28T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallSpecial values of adjoint L-functions and congruences for automorphic forms on GL(n) over a number field2017-05-03text/htmlen-USThe Johns Hopkins University PressSpecial values of adjoint L-functions and congruences for automorphic forms on GL(n) over a number field2017-05-032017TWOProject MUSE®420602017-07-28T00:00:00-05:002017-05-03Group C*-algebras as decreasing intersection of nuclear C*-algebras
http://muse.jhu.edu/article/657766
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We prove that for every exact discrete group Γ, there is an intermediate C*-algebra between the reduced group C*-algebra and the intersection of the group von Neumann algebra and the uniform Roe algebra which is realized as the intersection of a decreasing sequence of isomorphs of the Cuntz algebra O2. In particular, when Γ has the AP (approximation property), the reduced group C*-algebra is realized in this way. We also study extensions of the reduced free group C*-algebras and show that any exact absorbing or unital absorbing extension of it by any stable separable nuclear C*-algebra is realized in this
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Project MUSE®http://muse.jhu.edu/2017-07-28T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallGroup C*-algebras as decreasing intersection of nuclear C*-algebras2017-05-03text/htmlen-USThe Johns Hopkins University PressGroup C*-algebras as decreasing intersection of nuclear C*-algebras2017-05-032017TWOProject MUSE®241392017-07-28T00:00:00-05:002017-05-03On moments of twisted L-functions
http://muse.jhu.edu/article/657767
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We study the average of the product of the central values of two L-functions of modular forms f and g twisted by Dirichlet characters to a large prime modulus q. As our principal tools, we use spectral theory to develop bounds on averages of shifted convolution sums with differences ranging over multiples of q, and we use the theory of Deligne and Katz to prove new bounds on bilinear forms in Kloosterman sums with power savings when both variables are near the square root of q. When at least one of the forms f and g is non-cuspidal, we obtain an asymptotic formula for the mixed second moment of twisted L-functions with a power saving error term. In particular, when both are non-cuspidal, this gives a significant
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Project MUSE®http://muse.jhu.edu/2017-07-28T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallOn moments of twisted L-functions2017-05-03text/htmlen-USThe Johns Hopkins University PressOn moments of twisted L-functions2017-05-032017TWOProject MUSE®273232017-07-28T00:00:00-05:002017-05-03Vertexwise criteria for admissibility of alcoves
http://muse.jhu.edu/article/657768
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We give a new description of the set Adm(μ) of admissible alcoves as an intersection of certain "obtuse cones" of alcoves, and we show this description may be given by imposing conditions vertexwise. We use this to prove the vertexwise admissibility conjecture of Pappas-Rapoport-Smithling. The same idea gives simple proofs of two ingredients used in the proof of the Kottwitz-Rapoport conjecture on existence of crystals with additional
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Project MUSE®http://muse.jhu.edu/2017-07-28T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallVertexwise criteria for admissibility of alcoves2017-05-03text/htmlen-USThe Johns Hopkins University PressVertexwise criteria for admissibility of alcoves2017-05-032017TWOProject MUSE®207702017-07-28T00:00:00-05:002017-05-03Cube sum problem and an explicit Gross-Zagier formula
http://muse.jhu.edu/article/657769
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A nonzero rational number is called a cube sum if it is of the form a3 + b3 with a, b ∈ ℚ×. In this paper, we prove that for any odd integer k ≥ 1, there exist infinitely many cube-free odd integers n with exactly k distinct prime factors such that 2n is a cube sum (resp. not a cube sum). We present also a general construction of Heegner points and obtain an explicit Gross-Zagier formula which is used to prove the Birch and Swinnerton-Dyer conjecture for certain elliptic curves related to the cube sum
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Project MUSE®http://muse.jhu.edu/2017-07-28T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallCube sum problem and an explicit Gross-Zagier formula2017-05-03text/htmlen-USThe Johns Hopkins University PressCube sum problem and an explicit Gross-Zagier formula2017-05-032017TWOProject MUSE®159102017-07-28T00:00:00-05:002017-05-03Strichartz and localized energy estimates for the wave equation in strictly concave domains
http://muse.jhu.edu/article/657770
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We prove localized energy estimates for the wave equation in domains with a strictly concave boundary when homogeneous Dirichlet or Neumann conditions are imposed. By restricting the solution to small, frequency dependent, space time collars of the boundary, it is seen that a stronger gain in regularity can be obtained relative to the usual energy estimates. Mixed norm estimates of Strichartz and square function type follow as a result, using the energy estimates to control error terms which arise in a wave packet parametrix construction. While the latter estimates are not new for Dirichlet conditions, the present approach provides an avenue for treating these estimates when Neumann conditions are imposed. The
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Project MUSE®http://muse.jhu.edu/2017-07-28T00:00:00-05:00http://muse.jhu.edu/journal/5/image/coversmallStrichartz and localized energy estimates for the wave equation in strictly concave domains2017-05-03text/htmlen-USThe Johns Hopkins University PressStrichartz and localized energy estimates for the wave equation in strictly concave domains2017-05-032017TWOProject MUSE®249562017-07-28T00:00:00-05:002017-05-03