On Some Weighted Average Values of L-functions

Let $q\ge 2$ and $N\ge 1$ be integers. W. Zhang (2008) has shown that for any fixed $\epsilon> 0$, and $q^{\epsilon} \le N \le q^{1/2 -\epsilon}$, $$\sum_{\chi \ne \chi_0} |\sum_{n=1}^N \chi(n)|^2 |L(1, \chi)|^2 = (1 + o(1)) \alpha_q q N$$ where the sum is take over all nonprincipal characters $\chi$ modulo $q$, $L(s, \chi)$ is the $L$-functions $L(1, \chi)$ corresponding to $\chi$ and $\alpha_q = q^{o(1)}$ is some explicit function of $q$. Here we show that the same formula holds in the range $q^{\epsilon} \le N \le q^{1 -\epsilon}$.Comment: Bull. Aust. Math. Soc. (to appear

Persistence of Kardar-Parisi-Zhang Interfaces

The probabilities $P_\pm(t_0,t)$ that a growing Kardar-Parisi-Zhang interface remains above or below the mean height in the time interval $(t_0, t)$ are shown numerically to decay as $P_\pm \sim (t_0/t)^{\theta_\pm}$ with $\theta_+ = 1.18 \pm 0.08$ and $\theta_- = 1.64 \pm 0.08$. Bounds on $\theta_\pm$ are derived from the height autocorrelation function under the assumption of Gaussian statistics. The autocorrelation exponent $\bar \lambda$ for a $d$--dimensional interface with roughness and dynamic exponents $\beta$ and $z$ is conjectured to be $\bar \lambda = \beta + d/z$. For a recently proposed discretization of the KPZ equation we find oscillatory persistence probabilities, indicating hidden temporal correlations.Comment: 4 pages, 3 figures, uses revtex and psfi

High dimensional behavior of the Kardar-Parisi-Zhang growth dynamics

We investigate analytically the large dimensional behavior of the Kardar-Parisi-Zhang (KPZ) dynamics of surface growth using a recently proposed non-perturbative renormalization for self-affine surface dynamics. Within this framework, we show that the roughness exponent $\alpha$ decays not faster than $\alpha\sim 1/d$ for large $d$. This implies the absence of a finite upper critical dimension.Comment: RevTeX, 4 pages, 2 figures. To appear in Phys. Rev.

Transculturating the modern : Zhang Ruogu\u27s literary life in 1930s Shanghai

Zhang Ruogu 張若谷(1905-1967), now known primarily as an urban writer,2 began his literary career by translating and commenting on French literature in newspapers and journals and subsequently published several urban stories. He was also an active advocate of urban life and played an important role in the introduction of the ideas of the French-style café gathering and European cultural trends. Zhang Ruogu’s literary activities, his admiration of French literature and culture, and his works inspired by the French literary works that he admired or translated, are the focus of investigation of this paper. From Paris to Shanghai and from 19th-century French literature to urban stories of Shanghai of the 1930s, these literary trends and works advanced through a process of translation and interpretation. What occurred during this translation and interpretation process? How does this examination aid us in understanding Zhang Ruogu’s own work and modern Chinese literature? This paper addresses Zhang Ruogu’s translations, adaptations and interpretations of French literature as well as his own literary works