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1.
By using specific subsequences of two different types of generalized Stern polynomials, we obtain several related classes of finite and infinite continued fractions involving a single term \(z^{t^j}\) in their partial numerators, where z is a complex variable and t is a positive integer. This approach is extended to other, sparser, subsequences of Stern polynomials, based on certain Lucas functions; this then leads to further infinite classes of continued fractions.  相似文献   
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We prove a formula, with power savings, for the sixth moment of Dirichlet L- functions averaged over all primitive characters χ (mod q) with q ≤?Q, and over the critical line. Our formula agrees precisely with predictions motivated by random matrix theory. In particular, the constant 42 appears as a factor in the leading order term, exactly as is predicted for the sixth moment of the Riemann zeta-function.  相似文献   
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We investigate the moments of the derivative, on the unit circle, of characteristic polynomials of random unitary matrices and use this to formulate a conjecture for the moments of the derivative of the Riemann ζ function on the critical line. We do the same for the analogue of Hardy’s Z-function, the characteristic polynomial multiplied by a suitable factor to make it real on the unit circle. Our formulae are expressed in terms of a determinant of a matrix whose entries involve the I-Bessel function and, alternately, by a combinatorial sum.  相似文献   
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Previous research has identified a "synchrony window" of several hundred milliseconds over which auditory-visual (AV) asynchronies are not reliably perceived. Individual variability in the size of this AV synchrony window has been linked with variability in AV speech perception measures, but it was not clear whether AV speech perception measures are related to synchrony detection for speech only or for both speech and nonspeech signals. An experiment was conducted to investigate the relationship between measures of AV speech perception and AV synchrony detection for speech and nonspeech signals. Variability in AV synchrony detection for both speech and nonspeech signals was found to be related to variability in measures of auditory-only (A-only) and AV speech perception, suggesting that temporal processing for both speech and nonspeech signals must be taken into account in explaining variability in A-only and multisensory speech perception.  相似文献   
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Simple Zeros of the Riemann Zeta-Function   总被引:1,自引:0,他引:1  
Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.  相似文献   
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 We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in three equivalent forms: as a determinant sum (and hence in terms of symmetric polynomials), as a combinatorial sum, and as a multiple contour integral. These formulae are analogous to those previously obtained for the Gaussian ensembles of Random Matrix Theory, but in this case are identities for any size of matrix, rather than large-matrix asymptotic approximations. They also mirror exactly the autocorrelation formulae conjectured to hold for L-functions in a companion paper. This then provides further evidence in support of the connection between Random Matrix Theory and the theory of L-functions. Received: 1 August 2002 / Accepted: 25 December 2002 Published online: 7 May 2003 Communicated by P. Sarnak  相似文献   
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Explicit lower bounds for the proportion of zeros of the derivatives of Riemann's ξ-function on the critical line are given. In particular, it is shown that the proportion tends to one as the order of the derivative tends to infinity.  相似文献   
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