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作者：Petersen, CL; Zakeri, S
摘要：Let 0 < theta < 1 be an irrational number with continued fraction expansion theta = [a(1),a(2),a(3),...], and consider the quadratic polynomial P-theta : z --> e(2piitheta)z + z(2). By performing a trans-quasiconformal surgery on an associated Blaschke product model, we prove that if log a(n) = O(rootn) as n --> infinity, then the Julia set of P-theta is locally connected and has Lebesgue measure zero. In particular, it follows that for almost every 0 < theta < 1, the quadratic P-theta has a S...
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作者：Agrawal, M; Kayal, N; Saxena, N
摘要：We present an unconditional deterministic polynomial-time algorithm that determines whether an input number is prime or composite.
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作者：Dembo, A; Peres, Y; Rosen, J; Zeitouni, O
摘要：Let T(x, epsilon) denote the first hitting time of the disc of radius epsilon centered at x for Brownian motion on the two dimensional torus T-2. We prove that SUPx epsilon T2 T(x, epsilon)/vertical bar log epsilon vertical bar(2) - 2/pi as epsilon -> 0. The same applies to Brownian motion on any smooth, compact connected, two-dimensional, Riemannian manifold with unit area and no boundary. As a consequence, we prove a conjecture, due to Aldous (1989), that the number of steps it takes a simpl...
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作者：Jacquet, H
摘要：We prove an identity of Kloosterman integrals which is the fundamental lemma of a relative trace formula for the general linear group in n variables.
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作者：Bray, HL; Neves, A
摘要：In this paper we compute the a-invariants (sometimes also called the smooth Yamabe invariants) of RP3 and RP2 X S-1 (which are equal) and show that the only prime 3-manifolds with larger a-invariants are S-3, S-2 x S-1, and S-2 x S-1 (the nonorientable S-2 bundle over S-1). More generally, we show that any 3-manifold with sigma-invariant greater than RP3 is either S-3, a connect sum with an S-2 bundle over S-1, or has more than one nonorientable prime component. A corollary is the Poincare con...
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作者：Grinberg, EL; Rubin, B
摘要：We study the Radon transform Rf of functions on Stiefel and Grassmann manifolds. We establish a connection between Rf and G (a) over circle rding-Gindikin fractional integrals associated to the cone of positive definite matrices. By using this connection, we obtain Abel-type representations and explicit inversion formulae for Rf and the corresponding dual Radon transform. We work with the space of continuous functions and also with L-p spaces.
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作者：Grafakos, L; Li, XC
摘要：It is shown that the bilinear Hilbert transforms H-alpha,H-beta(f, g) (x) = p. v. integral(R) f(x - alphat)g(x - betat) dt/t map L-p1(R) x L-p2(R) --> L-p(R) uniformly in the real parameters alpha,beta when 2 < p(1),p(2) < infinity and 1 < p = p(1)p(2)/p(1)+p(2) < 2. Combining this result with the main result in [9], we deduce that the operators H-1,H-alpha map L-2(R) x L-infinity(R) --> L-2(R) uniformly in the real parameter alpha is an element of [0, 1]. This completes a program initiated by...
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作者：Bhargava, M
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作者：Krötz, B; Stanton, RJ
摘要：Let G be a connected, real, semisimple Lie group contained in its complexification G(C), and let K be a maximal compact subgroup of G. We construct a K-C-G double coset domain in G(C), and we show that the action of G on the K-finite vectors of any irreducible unitary representation of G has a holomorphic extension to this domain. For the resultant holomorphic extension of K-finite matrix coefficients we obtain estimates of the singularities at the boundary, as well as majorant/minorant estima...
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作者：Bonahon, F; Otal, JP
