Annals of Mathematics

最新文章

• The bilinear maximal functions map into Lp for 2/3 < p ≤ 1 AI翻译
  作者：Lacey, MT
  摘要：The bilinear maximal operator defined below maps L-p x L-q into L-r provided 1 < p, q < infinity, 1/p + 1/q = 1/r and 2/3 < r less than or equal to 1. Mfg(x) = sup(t>0) 1/2t integral(-t)(t) \f(x + y)g(x - y)\ dy. In particular Mfg is integrable if f and g are square integrable, answering a conjecture posed by Alberto Calderon.
• A proof of Pisot's dth root conjecture AI翻译
  作者：Zannier, U
  摘要：Let {b(n) : n is an element of N} be the sequence of coefficients in the Taylor expansion of a rational function R(X) is an element of Q(X) and suppose that b(n) is a perfect d(th) power for all large n. A conjecture of Pisot states that one can choose a d(th) root a(n) of b(n) such that Sigma a(n)X-n is also a rational function. Actually, this is the fundamental case of an analogous statement formulated for fields more general than Q. A number of papers have been devoted to various special ca...
• Analytic properties of zeta functions and subgroup growth AI翻译
  作者：du Sautoy, M; Grunewald, F
• On nonperturbative localization with quasi-periodic potential AI翻译
  作者：Bourgain, J; Goldstein, M
• The uncountable spectra of countable theories AI翻译
  作者：Hart, B; Hrushovski, E; Laskowski, MC
  摘要：Let T be a complete, first-order theory in a finite or countable language having infinite models. Let I(T, kappa) be the number of isomorphism types of models of T of cardinality kappa. We denote by mu (respectively <()over cap>) the number of cardinals (respectively infinite cardinals) less than or equal to kappa.
• Index theorem of p-adic differential equations .3. AI翻译
  作者：Christol, G; Mebkhout, Z
• A remarkable periodic solution of the three-body problem in the case of equal masses AI翻译
  作者：Chenciner, A; Montgomery, R
  摘要：Using a variational method, we exhibit a surprisingly simple periodic or-bit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising feature is that the three bodies chase each other around a fixed eight-shaped curve. Setting aside collinear motions, the only other known motion along a fixed curve in the inertial plane is the Lagrange relative equilibrium in which the three bodies form a rigid equil...
• A new approach to inverse spectral theory, II. General real potentials and the connection to the spectral measure AI翻译
  作者：Gesztesy, F; Simon, B
  摘要：We continue the study of the A-amplitude associated to a half-line Schrodinger operator, -d(2)/dx(2) + q in L-2((0, b)), b less than or equal to infinity. A is related to the Weyl-Titchmarsh m-function via m(-kappa (2)) = -kappa-integral (a)(0) A(alpha )e(-2 alpha kappa) d alpha +O(e(-(2a-epsilon)kappa)) for all epsilon > 0. We discuss five issues here. First, we extend the theory to general q in L-1((0, a)) for all a, including q's which are limit circle at infinity. Second, we prove the foll...
• Real algebraic curves, the moment map and amoebas AI翻译
  作者：Mikhalkin, G
  摘要：In this paper we prove the topological uniqueness of maximal arrangements of a real plane algebraic curve with respect to three lines. More generally, we prove the topological uniqueness of a maximally arranged algebraic curve on a real toric surface. We use the moment map as a tool for studying the topology of real algebraic curves and their complexifications.
• Proof of the gradient conjecture of R.!Thom AI翻译
  作者：Kurdyka, K; Mostowski, T; Parusinski, A
  摘要：Let x(t) be a trajectory of the gradient of a real analytic function and suppose that to is a limit point of x(t). We prove the gradient conjecture of R. Them which states that the secants of x(t) at to have a limit. Actually we show a stronger statement: the radial projection of x(t) from to onto the unit sphere has finite length.