منابع مشابه
On the transcendence of certain Petersson inner products
We show that for all normalized Hecke eigenforms $f$ with weight one and of CM type, the number $(f,f)$ where $(cdot, cdot )$ denotes the Petersson inner product, is a linear form in logarithms and hence transcendental.
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The Monge-Kantorovich mass transport problem is to find the transport plan that minimizes the cost (1). This was formulated by Kantorovich in the 1940's, generalizing Monge's format in 1781. Monge's original formulation of the problem assumes that and asks for BßC œ lBCl a b the existence of a mass-preserving map from the support, Spt ,of 0 a b . . to Spt that minimizes a b / the cost ( a b a ...
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We present a simple, natural #P -complete problem. Let G be a directed graph, and let k be a positive integer. We define q(G; k) as follows. At each vertex v, we place a k-dimensional complex vector xv. We take the product, over all edges (u, v), of the inner product 〈xu, xv〉. Finally, q(G; k) is the expectation of this product, where the xv are chosen uniformly and independently from all vecto...
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A general model for optimal location problems is given and the existence of solutions is proved under practical conditions. Conditions that all possible solutions must satisfy are given; these conditions form the basis of a method of finding solutions.
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In this paper we consider the sequence of monic polynomials (Qn) orthogonal with respect to a symmetric Sobolev inner product. If Q2n(x) = Pn(x) and Q2n+1(x) = xRn(x), then we deduce the integral representation of the inner products such that (Pn) and (Rn) are, respectively, the corresponding sequences of monic orthogonal polynomials. In the semiclassical case, algebraic relations between such ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1997
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5287