On the mean values of L-functions in orthogonal and symplectic families

Hybrid Euler-Hadamard products have previously been studied for the Riemann zeta function on its critical line and for Dirichlet L-functions in the context of the calculation of moments and connections with Random Matrix Theory. According to the Katz-Sarnak classification, these are believed to represent families of L-function with unitary symmetry. We here extend the formalism to families with orthogonal & symplectic symmetry. Specifically, we establish formulae for real quadratic Dirichlet L-functions and for the L-functions associated with primitive Hecke eigenforms of weight 2 in terms of partial Euler and Hadamard products. We then prove asymptotic formulae for some moments of these partial products and make general conjectures based on results for the moments of characteristic polynomials of random matrices

On Balazard, Saias, and Yor's equivalence to the Riemann Hypothesis

Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero. Assuming the Riemann Hypothesis, we investigate the rate at which a truncated version of this integral tends to zero, answering a question of Borwein, Bradley, and Crandall and disproving a conjecture of the same authors. A simple modification of our techniques gives a new proof of a classical Omega theorem for the function S(t) in the theory of the Riemann zeta-function.Comment: 11 page

On the variance of sums of arithmetic functions over primes in short intervals and pair correlation for L-functions in the Selberg class

We establish the equivalence of conjectures concerning the pair correlation of zeros of $L$-functions in the Selberg class and the variances of sums of a related class of arithmetic functions over primes in short intervals. This extends the results of Goldston & Montgomery [7] and Montgomery & Soundararajan [11] for the Riemann zeta-function to other $L$-functions in the Selberg class. Our approach is based on the statistics of the zeros because the analogue of the Hardy-Littlewood conjecture for the auto-correlation of the arithmetic functions we consider is not available in general. One of our main findings is that the variances of sums of these arithmetic functions over primes in short intervals have a different form when the degree of the associated $L$-functions is 2 or higher to that which holds when the degree is 1 (e.g. the Riemann zeta-function). Specifically, when the degree is 2 or higher there are two regimes in which the variances take qualitatively different forms, whilst in the degree-1 case there is a single regime

Toward Affective Dialogue Modeling using Partially Observable Markov Decision Processes

We propose a novel approach to developing a dialogue model which is able to take into account some aspects of the user’s emotional state and acts appropriately. The dialogue model uses a Partially Observable Markov Decision Process approach with observations composed of the observed user’s emotional state and action. A simple example of route navigation is explained to clarify our approach and preliminary results & future plans are briefly discussed

The influence of oscillations on energy estimates for damped wave models with time-dependent propagation speed and dissipation

The aim of this paper is to derive higher order energy estimates for solutions to the Cauchy problem for damped wave models with time-dependent propagation speed and dissipation. The model of interest is \begin{equation*} u_{tt}-\lambda^2(t)\omega^2(t)\Delta u +\rho(t)\omega(t)u_t=0, \quad u(0,x)=u_0(x), \,\, u_t(0,x)=u_1(x). \end{equation*} The coefficients $\lambda=\lambda(t)$ and $\rho=\rho(t)$ are shape functions and $\omega=\omega(t)$ is an oscillating function. If $\omega(t)\equiv1$ and $\rho(t)u_t$ is an "effective" dissipation term, then $L^2-L^2$ energy estimates are proved in [2]. In contrast, the main goal of the present paper is to generalize the previous results to coefficients including an oscillating function in the time-dependent coefficients. We will explain how the interplay between the shape functions and oscillating behavior of the coefficient will influence energy estimates.Comment: 37 pages, 2 figure

An improved time of flight gamma-ray telescope to monitor diffuse gamma-ray in the energy range 5 MeV - 50 MeV

A time of flight measuring device is the basic triggering system of most of medium and high energy gamma-ray telescopes. A simple gamma-ray telescope has been built in order to check in flight conditions the functioning of an advanced time of flight system. The technical ratings of the system are described. This telescope has been flown twice with stratospheric balloons, its axis being oriented at various Zenital directions. Flight results are presented for diffuse gamma-rays, atmospheric secondaries, and various causes of noise in the 5 MeV-50 MeV energy range