Rankin-Selberg periods for spherical principal series

By the unfolding method, Rankin-Selberg L-functions for ${\rm GL}(n)\times{\rm GL}(m)$ can be expressed in terms of period integrals. These period integrals actually define invariant forms on tensor products of the relevant automorphic representations. By the multiplicity-one theorems due to Sun-Zhu and Chen-Sun such invariant forms are unique up to scalar multiples and can therefore be related to invariant forms on equivalent principal series representations. We construct meromorphic families of such invariant forms for spherical principal series representations of ${\rm GL}(n,\mathbb{R})$ and conjecture that their special values at the spherical vectors agree in absolute value with the archimedean local L-factors of the corresponding L-functions. We verify this conjecture in several cases. This work can be viewed as the first of two steps in a technique due to Bernstein-Reznikov for estimating L-functions using their period integral expressions.Comment: 25 pages. v3 replaces the previous versions which have a gap in Lemma 4.1 due to the non-co-compactness of the lattic

Novel Two-dimensional Carbon Allotrope with Strong Electronic Anisotropy

Two novel two-dimensional carbon allotropes comprised of octagons and pentagons are proposed based on the first-principles calculations. The two carbon allotropes, named OPG-L and OPG-Z, are found to have distinct properties. OPG-L is metallic, while OPG-Z is a gapless semimetal. Remarkably, OPG-Z exhibits pronounced electronic anisotropy with highly anisotropic Dirac points at the Fermi level. A tight-binding model is suggested to describe the low-energy quasiparticles, which clarifies the origin of the anisotropic Dirac points. Such an anisotropic electronic characteristic of OPG-Z is expected to have wide implications in nano-electronics.Comment: 6 pages, 5 figures (accepted by Physical Review B

To Be or Not To Be Humorous? Cross Cultural Perspectives on Humor

open access articleHumor seems to manifest differently in Western and Eastern cultures, although little is known about how culture shapes humor perceptions. The authors suggest that Westerners regard humor as a common and positive disposition; the Chinese regard humor as a special disposition particular to humorists, with controversial aspects. In Study 1, Hong Kong participants primed with Western culture evaluate humor more positively than they do when primed with Chinese culture. In Study 2a, Canadians evaluate humor as being more important in comparison with Chinese participants. In Study 2b, Canadians expect ordinary people to possess humor, while Chinese expect specialized comedians to be humorous. The implications and limitations are discussed