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作者：Dokchitser, Tim; Dokchitser, Vladimir
摘要：Let A be an abelian variety over a number field K. An identity between the L-functions L (A/K-i, s) for extensions K-i of K induces a conjectural relation between the Birch-Swinnerton-Dyer quotients. We prove these relations modulo finiteness of X, and give an analogous statement for Selmer groups. Based on this, we develop a method for determining the parity of various combinations of ranks of A over extensions of K. As one of the applications, we establish the parity conjecture for elliptic ...
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作者：Bouw, Irene I.; Moeller, Martin
摘要：We construct a Teichmuller curve uniformized by a Fuchsian triangle group commensurable to Delta(m, n, infinity) for every m, n <= infinity. In most cases, for example when m not equal n and m or n is odd, the uniformizing group is equal to the triangle group Delta(m, n, infinity). Our construction includes the Teichmuller curves constructed by Veech and Ward as special cases. The construction essentially relies on properties of hypergeometric differential operators. For small m, we find billi...
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作者：Poonen, Bjorn
摘要：Let k be any global field of characteristic not 2. We construct a k-variety X such that X(k) is empty, but for which the emptiness cannot be explained by the Brauer-Manin obstruction or even by the Brauer-Manin obstruction applied to finite etale covers.
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作者：Caffarelli, Luis A.; McCann, Robert J.
摘要：Given compactly supported 0 <= f; g is an element of L-1 (R-n), the problem of transporting a fraction m <= min{parallel to f parallel to(L)1, parallel to g parallel to (L)1} of the mass of f onto g as cheaply as possible is considered, where cost per unit mass transported is given by a cost function c, typically quadratic c(x, y) = vertical bar x - y vertical bar(2)/2. This question is shown to be equivalent to a double obstacle problem for the Monge-Ampere equation, for which sufficient cond...
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作者：Chen, Gui-Qiang; Feldman, Mikhail
摘要：When a plane shock hits a wedge head on, it experiences a reflection-diffraction process and then a self-similar reflected shock moves outward as the original shock moves forward in time. Experimental, computational, and asymptotic analysis has shown that various patterns of shock reflection may occur, including regular and Mach reflection. However, most of the fundamental issues for shock reflection have not been understood, including the global structure, stability, and transition of the dif...
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作者：Marklof, Jens; Strombergsson, Andreas
摘要：The periodic Lorentz gas describes the dynamics of a point particle in a periodic array of spherical scatterers, and is one of the fundamental models for chaotic diffusion. In the present paper we investigate the Boltzmann-Grad limit, where the radius of each scatterer tends to zero, and prove the existence of a limiting distribution for the free path length. We also discuss related problems, such as the statistical distribution of directions of lattice points that are visible from a fixed pos...
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作者：Green, Benjamin; Tao, Terence
摘要：Consider a system Psi of nonconstant affine-linear forms psi(1),...,psi(t) : Z(d) -> Z, no two of which are linearly dependent. Let N be a large integer, and let K subset of [-N, N](d) be convex. A generalisation of a famous and difficult open conjecture of Hardy and Littlewood predicts an asymptotic, as N -> infinity, for the number of integer points n is an element of Z(d) boolean AND K for which the integers psi(1)(n),...,psi(t)(n) are simultaneously prime. This implies many other well-know...
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作者：Rugh, Hans Henrik
摘要：We introduce complex cones and associated projective gauges, generalizing a real Birkhoff cone and its Hilbert metric to complex vector spaces. We deduce a variety of spectral gap theorems in complex Banach spaces. We prove a dominated complex cone contraction theorem and use it to extend the classical Perron-Frobenius Theorem to complex matrices, Jentzsch's Theorem to complex integral operators, a Krein-Rutman Theorem to compact and quasi-compact complex operators and a Ruelle-Perron-Frobeniu...
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作者：Pop, Florian
摘要：In this note we show that the quotient field of a domain which is Henselian with respect to a nontrivial ideal is a large field, and give some applications of this fact, using a specialization theorem for ramified covers of the line over (generalized) Krull fields.
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作者：Viehweg, Eckart
摘要：Let M-h be the moduli scheme of canonically polarized manifolds with Hilbert polynomial h. We construct for nu >= 2 with h(nu) > 0 a projective compactification (M) over bar (h) of the reduced moduli scheme (M-h)(red) such that the ample invertible sheaf lambda(nu), corresponding to det(f(*)omega(nu)(X0/Y0)) on the moduli stack, has a natural extension (lambda) over bar (nu) is an element of Pic((M) over bar (h))(Q). A similar result is shown for moduli of polarized minimal models of Kodaira d...
