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作者：Deng, Yu; Nahmod, Andrea R.; Yue, Haitian
作者单位：University of Southern California; University of Massachusetts System; University of Massachusetts Amherst; ShanghaiTech University
摘要：We introduce the theory of random tensors, which naturally extends the method of random averaging operators in our earlier work (Deng et al. in: Invariant Gibbs measures and global strong solutions for 4009 nonlinear Schrodinger equations in dimension two, ), to study the propagation of randomness under nonlinear dispersive equations. By applying this theory we establish almost-sure local well-posedness for semilinear Schrodinger equations in the full subcritical range relative to the probabil...
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作者：Sawin, Will; Shusterman, Mark
作者单位：Columbia University; Harvard University
摘要：We establish cancellation in short sums of certain special trace functions over F-q [u] belowthe Polya-Vinogradov range, with savings approaching square-root cancellation as q grows. This is used to resolve the F-q [u]-analog of Chowla's conjecture on cancellation in Mobius sums over polynomial sequences, and of the Bateman-Horn conjecture in degree 2, for some values of q. A final application is to sums of trace functions over primes in F-q [u].
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作者：Dunfield, Nathan M.; Garoufalidis, Stavros; Rubinstein, J. Hyam
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Southern University of Science & Technology; University of Melbourne
摘要：We consider the natural problem of counting isotopy classes of essential surfaces in 3-manifolds, focusing on closed essential surfaces in a broad class of hyperbolic 3-manifolds. Our main result is that the count of (possibly disconnected) essential surfaces in terms of their Euler characteristic always has a short generating function and hence has quasi-polynomial behavior. This gives remarkably concise formulae for the number of such surfaces, as well as detailed asymptotics. We give algori...
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作者：Ghosh, Amit; Sarnak, Peter
作者单位：Oklahoma State University System; Oklahoma State University - Stillwater; Institute for Advanced Study - USA; Princeton University
摘要：For integers k, we consider the affine cubic surface V-k given by M(x) = x(1)(2) + x(2)(2) + x(3)(2) - x(1)x(2)x(3) = k. We show that for almost all k the Hasse Principle holds, namely that V-k(Z) is non-empty if V-k(Z(p)) is non-empty for all primes p, and that there are infinitely many k's for which it fails. The Markoff morphisms act on V-k(Z) with finitely many orbits and a numerical study points to some basic conjectures about these class numbers and Hasse failures. Some of the analysis m...
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作者：Angles, Bruno; Tuan Ngo Dac; Ribeiro, Floric Tavares
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Caen Normandie
摘要：In 2012 Taelman proved a class formula for Drinfeld F-q[t]-modules. For an arbitrary coefficient ring A, several deep but partial results in the direction of a class formula for Drinfeld A-modules have been obtained. In this paper, using a completely new approach based on the notion of Stark units, we establish the class formula for Drinfeld A-modules in full generality. Further we extend this class formula for A-finite or abelian Anderson modules and more generally for admissible Anderson mod...
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作者：Carrasco, Matias; Mackay, John M.
作者单位：Universidad de la Republica, Uruguay; University of Bristol
摘要：We study the (Ahlfors regular) conformal dimension of the boundary at infinity of Gromov hyperbolic groups which split over elementary subgroups. If such a group is not virtually free, we show that the conformal dimension is equal to the maximal value of the conformal dimension of the vertex groups, or 1, whichever is greater, and we characterise when the conformal dimension is attained. As a consequence, we are able to characterise which Gromov hyperbolic groups (without 2-torsion) have confo...
