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作者：Hall, J. I.
摘要：A group is locally finite if every finite subset generates a finite subgroup. A group of linear transformations is finitary if each element minus the identity is an endomorphism of finite rank. The classification and structure theory for locally finite simple groups splits naturally into two cases-those groups that can be faithfully represented as groups of finitary linear transformations and those groups that are not finitary linear. This paper completes the finitary case. We classify up to i...
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作者：Anderson, J. M.; Eiderman, V. Ya.
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作者：Talagrand, Michel
摘要：Using Guerra's interpolation scheme, we compute the free energy of the Sherrington-Kirkpatrick model for spin glasses at any temperature, confirming a celebrated prediction of G. Parisi.
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作者：Einsiedler, Manfred; Katok, Anatole; Lindenstrauss, Elon
摘要：We classify the measures on SL(k,R)/SL(k,Z) which are invariant and ergodic under the action of the group A of positive diagonal matrices with positive entropy. We apply this to prove that the set of exceptions to Littlewood's conjecture has Hausdorff dimension zero.
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作者：Bugeaud, Yann; Mignotte, Maurice; Siksek, Samir
摘要：This is the first in a series of papers whereby we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of Fermat's Last Theorem. In this paper we give new improved bounds for linear forms in three logarithms. We also apply a combination of classical techniques with the modular approach to show that the only perfect powers in the Fibonacci sequence are 0, 1, 8 and 1...
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作者：Finis, Tobias
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作者：Ellenberg, Jordan S.; Venkatesh, Akshay
摘要：We give an upper bound on the number of extensions of a fixed number field of prescribed degree and discriminant <= X; these bounds improve on work of Schmidt. We also prove various related results, such as lower bounds for the number of extensions and upper bounds for Galois extensions.
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作者：Lindenstrauss, Elon
摘要：We classify measures on the locally homogeneous space Gamma\SL(2, R) x L which are invariant and have positive entropy under the diagonal subgroup of SL(2,R) and recurrent under L. This classification can be used to show arithmetic quantum unique ergodicity for compact arithmetic surfaces, and a similar but slightly weaker result for the finite volume case. Other applications are also presented. In the appendix, joint with D. Rudolph, we present a maximal ergodic theorem, related to a theorem ...
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作者：Dencker, Nils
摘要：We give a proof of the Nirenberg-Treves conjecture: that local solvability of principal-type pseudo-differential operators is equivalent to condition (T). This condition rules out sign changes from - to + of the imaginary part of the principal symbol along the oriented bicharacteristics of the real part. We obtain local solvability by proving a localizable a priori estimate for the adjoint operator with a loss of two derivatives (compared with the elliptic case). The proof involves a new metri...
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作者：Beukers, F.
摘要：Using Y. Andre's result on differential equations satisfied by E-functions, we derive an improved version of the Siegel-Shidlovskii theorem. It gives a complete characterisation of algebraic relations over the algebraic numbers between values of E-functions at any nonzero algebraic point.
