-
作者：Parnovski, Leonid; Sobolev, Alexander V.
作者单位：University of London; University College London
摘要：We consider a periodic self-adjoint pseudo-differential operator H=(-Delta) (m) +B, m > 0, in ae (d) which satisfies the following conditions: (i) the symbol of B is smooth in x, and (ii) the perturbation B has order less than 2m. Under these assumptions, we prove that the spectrum of H contains a half-line. This, in particular implies the Bethe-Sommerfeld conjecture for the Schrodinger operator with a periodic magnetic potential in all dimensions.
-
作者：Smillie, John; Weiss, Barak
作者单位：Ben-Gurion University of the Negev; Cornell University
摘要：We answer a question of Vorobets by showing that the lattice property for flat surfaces is equivalent to the existence of a positive lower bound for the areas of affine triangles. We show that the set of affine equivalence classes of lattice surfaces with a fixed positive lower bound for the areas of triangles is finite and we obtain explicit bounds on its cardinality. We deduce several other characterizations of the lattice property.
-
作者：Mazur, B.; Rubin, K.
作者单位：Harvard University; University of California System; University of California Irvine
摘要：In this paper we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields. We give sufficient conditions on an elliptic curve so that it has twists of arbitrary 2-Selmer rank, and we give lower bounds for the number of twists (with bounded conductor) that have a given 2-Selmer rank. As a consequence, under appropriate hypotheses we can find many twists with trivial Mordell-Weil group, and (assuming the Shafarevich-Tate conjecture) many other...
-
作者：Ng, Lenhard
作者单位：Duke University
摘要：We construct a combinatorial invariant of Legendrian knots in standard contact three-space. This invariant, which encodes rational relative Symplectic Field Theory and extends contact homology, counts holomorphic disks with an arbitrary number of positive punctures. The construction uses ideas from string topology.
-
作者：Pfitzner, Hermann
作者单位：Universite de Orleans
摘要：A boundary for a real Banach space is a subset of the dual unit sphere with the property that each element of the Banach space attains its norm on an element of that subset. Trivially, the pointwise convergence with respect to such a boundary is coarser than the weak topology on the Banach space. The boundary problem asks whether nevertheless both topologies have the same norm bounded compact sets. The main theorem of this paper states the equivalence of countable and sequential compactness of...
-
作者：Makarov, N.; Poltoratski, A.
作者单位：Texas A&M University System; Texas A&M University College Station; California Institute of Technology
摘要：We consider the family of Toeplitz operators T-J (S) over bara acting in the Hardy space H-2 in the upper halfplane; J and S are given meromorphic inner functions, and a is a real parameter. In the case where the argument of S has a power law type behavior on the real line, we compute the critical value c(J, S) = inf {a : ker T-J (S) over bara not equal 0}. The formula for c(J, S) generalizes the Beurling-Malliavin theorem on the radius of completeness for a system of exponentials.
-
作者：Blomer, Valentin; Holowinsky, Roman
作者单位：University of Toronto
摘要：Let f be an L (2)-normalized weight zero Hecke-Maa cusp form of square-free level N, character chi and Laplacian eigenvalue lambda a parts per thousand yen1/4. It is shown that aEuro-faEuro-(a)a parts per thousand(a) (lambda) N (-1/37), from which the hybrid bound aEuro-faEuro-(a)a parts per thousand(a)lambda (1/4)(N lambda)(-delta) (for some delta > 0) is derived. The first bound holds also for f=y (k/2) F where F is a holomorphic cusp form of weight k with the implied constant now depending ...
