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作者：Farber, M; Weinberger, S
摘要：We prove that the answer to the zero-in-the-spectrum conjecture, in the form suggested by J. Lott, is negative. Namely, we show that for any n greater than or equal to 6 there exists a closed n-dimensional smooth manifold A-P, so that zero does not belong to the spectrum of the Laplace-Beltrami operator acting on the L-2 forms of all degrees on the universal covering M.
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作者：Adler, M; van Moerbeke, P
摘要：Given the Hermitian, symmetric and symplectic ensembles, it is shown that the probability that the spectrum belongs to one or several intervals satisfies a nonlinear PDE. This is done for the three classical ensembles: Gaussian, Laguerre and Jacobi. For the Hermitian ensemble, the PDE (in the boundary points of the intervals) is related to the Toda lattice and the KP equation, whereas for the symmetric and symplectic ensembles the PDE is an inductive equation, related to the so-called Pfaff-KP...
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作者：Bavula, VV
摘要：THEOREM. Let R and T be somewhat commutative algebras with the same holonomic number and let phi : R --> T be an algebra homomorphism. Then every holonomic T-module M is (via phi) a holonomic R-module and has finite length as an R-module. When applied to the Weyl algebra this result gives a positive answer to a question of Rentschler. In the important case where R = D(X) and T = D(Y) are rings of differential operators on smooth irreducible algebraic affine varieties X and Y of the same dimens...
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作者：Cilleruelo, J; Sols, I
摘要：Let E be a semistable, rank two vector bundle of degree d on a Riemann surface C of genus g greater than or equal to 1, i.e. such that the minimal degree s of a tensor product of E with a line bundle having a nonzero section is nonnegative. We give an analogue of Clifford's lemma by showing that E has at most (d - s)/2 + delta independent sections, where 6 is 2 or 1 according to whether the Krawtchouk polynomial K-r(n, N) is zero or not at r = (d - s)/2 + 1, n = g, N = 2g - s (the analogous bo...
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作者：Frohardt, D; Magaard, K
摘要：The authors prove the 1990 conjecture of Guralnick and Thompson on composition factors of monodromy groups. Using Riemann's existence theorem, the conjecture translates into a problem on primitive permutation groups. This group theoretic problem had been reduced to a question about actions of classical groups on subspaces of their natural modules. The key ingredients in the present proof are the authors' earlier fixed point ratio estimates for such actions and a result of Scott on the generati...
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作者：Gardiner, FP; Lakic, N
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作者：Hertweck, M
摘要：Let X be a finite group, and denote its integral group ring by ZX. A group basis of ZX is a subgroup Y of the group of units of ZX of augmentation 1 such that ZX = ZY and /X/ = /Y/. An example of a finite group X is given such that ZX has a group basis which is not isomorphic to X. A main ingredient is the existence of a subgroup G of X which possesses a non-inner automorphism which becomes inner in the integral group ring ZG.
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作者：Wolff, T
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作者：Hoffmann, W
摘要：Weighted orbital integrals are distributions on reductive groups over local fields appearing both in the local and global trace formulas. There are associated invariant distributions, which play the same role in the invariant trace formulas. In the case of real groups, the Fourier transforms of these distributions satisfy a system of differential equations. As a step towards determining those Fourier transforms, we show that this system is holonomic and has a simple singularity at infinity. We...
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作者：Izhboldin, OT
摘要：Let F be a field of characteristic not equal 2. The u-invariant of the field F is defined as the maximum dimension of anisotropic quadratic forms over F. It is well-known that the u-invariant cannot be equal to 3, 5, or 7. We construct a field F with u-invariant 9. It is a first example of a field with odd u-invariant > 1. The proof uses the computation of the third Chow group of projective quadrics X-phi corresponding to quadratic forms phi. We compute CH3(X-phi) for all phi except for the ca...
