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作者：Hundertmark, Dirk; Kunstmann, Peer; Ried, Tobias; Vugalter, Semjon
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of Illinois System; University of Illinois Urbana-Champaign; Max Planck Society; Leipzig University
摘要：There are several proofs by now for the famous Cwikel-Lieb-Rozenblum (CLR) bound, which is a semiclassical bound on the number of bound states for a Schrodinger operator, proven in the 1970s. Of the rather distinct proofs by Cwikel, Lieb, and Rozenblum, the one by Lieb gives the best constant, the one by Rozenblum does not seem to yield any reasonable estimate for the constants, and Cwikel's proof is said to give a constant which is at least about 2 orders of magnitude off the truth. This situ...
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作者：Breuil, Christophe; Herzig, Florian; Hu, Yongquan; Morra, Stefano; Schraen, Benjamin
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; University of Toronto; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：Let p be a prime number, F a totally real number field unramified at places above p and D a quaternion algebra of center F split at places above p and at no more than one infinite place. Let v be a fixed place of F above p and r : Gal(F/F) ? GL(2)(F-p) an irreducible modular continuous Galois representation which, at the place v, is semisimple and sufficiently generic (and satisfies some weak genericity conditions at a few other finite places). We prove that many of the admissible smooth repre...
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作者：Bandeira, Afonso S. S.; Boedihardjo, March T. T.; van Handel, Ramon
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Princeton University
摘要：A central tool in the study of nonhomogeneous random matrices, the noncommutative Khintchine inequality, yields a nonasymptotic bound on the spectral norm of general Gaussian random matrices X = S-i g(i)A(i) where g(i) are independent standard Gaussian variables and A(i) are matrix coefficients. This bound exhibits a logarithmic dependence on dimension that is sharp when the matrices A(i) commute, but often proves to be suboptimal in the presence of noncommutativity. In this paper, we develop ...
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作者：Tsuzuki, Nobuo
作者单位：Tohoku University
摘要：The minimal slope conjecture, which was proposed by K. S. Kedlaya, asserts that two irreducible overconvergent F-isocrystals on a smooth variety are isomorphic to each other if both minimal slope constitutions of slope filtrations are isomorphic to each other. We affirmatively solve the minimal slope conjecture for overconvergent F-isocrystals on curves and for overconvergent (Q) over bar (p)-F-isocrystals on smooth varieties over finite fields.
