Uniform asymptotics for the full moment conjecture of the Riemann zeta function

Conrey, Farmer, Keating, Rubinstein, and Snaith, recently conjectured formulas for the full asymptotics of the moments of $L$-functions. In the case of the Riemann zeta function, their conjecture states that the $2k$-th absolute moment of zeta on the critical line is asymptotically given by a certain $2k$-fold residue integral. This residue integral can be expressed as a polynomial of degree $k^2$, whose coefficients are given in exact form by elaborate and complicated formulas. In this article, uniform asymptotics for roughly the first $k$ coefficients of the moment polynomial are derived. Numerical data to support our asymptotic formula are presented. An application to bounding the maximal size of the zeta function is considered.Comment: 53 pages, 1 figure, 2 table

Discovery of an Isolated Population of \u3ci\u3eAnax Longipes\u3c/i\u3e in Michigan (Odonata: Aeshnidae)

Anax longipes is a large aeshnid dragonfly previously unknown from Michigan. Adults and larvae were found in abundance at a series of experimental ponds within the E.S. George Reserve in Livingston County, Michigan

Public Health in the Age of Ebola in West Africa

The Ebola epidemic, with its fast-growing toll and real potential for spreading into much of Africa, including major cities, has the makings of a “Black Swan” event. Such events, using the term coined by Nassim Nicholas Taleb, are: 1) unpredictable, outside the realm of regular expectations; 2) have a major impact, and; 3) are rationalized after the fact as being explainable and predictable. We have learned from this outbreak the potential for an infectious disease to be politically, economically, and socially destabilizing, and that what kills us may be very different from what frightens us or substantially affects our social systems. This has important implications for resource allocation. Health threats like Ebola may not have historically have not killed large numbers of people, but because of possible scenarios under which they can have a devastating impact, require a greater share of limited resources, such as for developing a vaccine. More creative imagination is needed in considering future infectious disease scenarios and in planning accordingly. Further, this Ebola epidemic could transform global governance for health. It demonstrates the need for fundamental reform at the WHO, including for greater funding, as WHO\u27s response–unable to mobilize sufficient funding, too slow to declare this a Public Health Emergency of International Concern–indicates that the Organization is presently poorly positioned to fulfill its constitutional role as the global health authority. Meanwhile, the leadership role that the United Nations is assuming suggests the emergence of an era of direct United Nations engagement in health threats that could destabilize nations and regions

Range Extension of \u3ci\u3eStylogomphus Albistylus\u3c/i\u3e (Odonata: Gomphidae) for the Upper Peninsula of Michigan

Larvae, exuviae, and teneral adults of Stylogomphus albistylus (Hagen) were collected from Mountain Stream, within the boundaries of the Huron Mountain Club, in the Upper Peninsula of Michigan (Marquette County). This represents the first published report of this species from the Upper Peninsula of Michigan, and only the second recorded site for the state of Michigan

Identification of point defects in HVPE-grown GaN by steady-state and time-resolved photoluminescence

We have investigated point defects in GaN grown by HVPE by using steady-state and time-resolved photoluminescence (PL). Among the most common PL bands in this material are the red luminescence band with a maximum at 1.8 eV and a zero-phonon line (ZPL) at 2.36 eV (attributed to an unknown acceptor having an energy level 1.130 eV above the valence band), the blue luminescence band with a maximum at 2.9 eV (attributed to ZnGa), and the ultraviolet luminescence band with the main peak at 3.27 eV (related to an unknown shallow acceptor). In GaN with the highest quality, the dominant defect-related PL band at high excitation intensity is the green luminescence band with a maximum at about 2.4 eV. We attribute this band to transitions of electrons from the conduction band to the 0/+ level of the isolated CN defect. The yellow luminescence (YL) band, related to transitions via the −/0 level of the same defect, has a maximum at 2.1 eV. Another yellow luminescence band, which has similar shape but peaks at about 2.2 eV, is observed in less pure GaN samples and is attributed to the CNON complex. In semi-insulating GaN, the GL2 band with a maximum at 2.35 eV (attributed to VN) and the BL2 band with a maximum at 3.0 eV and the ZPL at 3.33 eV (attributed to a defect complex involving hydrogen) are observed. We also conclude that the gallium vacancy-related defects act as centers of nonradiative recombination