On Differences of Zeta Values

Finite differences of values of the Riemann zeta function at the integers are explored. Such quantities, which occur as coefficients in Newton series representations, have surfaced in works of Maslanka, Coffey, Baez-Duarte, Voros and others. We apply the theory of Norlund-Rice integrals in conjunction with the saddle point method and derive precise asymptotic estimates. The method extends to Dirichlet L-functions and our estimates appear to be partly related to earlier investigations surrounding Li's criterion for the Riemann hypothesis.Comment: 18 page

Partition function for a singular background

We present a method for evaluating the partition function in a varying external field. Specifically, we look at the case of a non-interacting, charged, massive scalar field at finite temperature with an associated chemical potential in the background of a delta-function potential. Whilst we present a general method, valid at all temperatures, we only give the result for the leading order term in the high temperature limit. Although the derivative expansion breaks down for inhomogeneous backgrounds we are able to obtain the high temperature expansion, as well as an analytic expression for the zero point energy, by way of a different approximation scheme, which we call the {\it local Born approximation} (LBA).Comment: 5 pages, 1 figure, revtex4, typos corrected. To appear in Phys. Lett.

Holonomies, anomalies and the Fefferman-Graham ambiguity in AdS3 gravity

Using the Chern-Simon formulation of (2+1) gravity, we derive, for the general asymptotic metrics given by the Fefferman-Graham-Lee theorems, the emergence of the Liouville mode associated to the boundary degrees of freedom of (2+1) dimensional anti de Sitter geometries. Holonomies are described through multi-valued gauge and Liouville fields and are found to algebraically couple the fields defined on the disconnected components of spatial infinity. In the case of flat boundary metrics, explicit expressions are obtained for the fields and holonomies. We also show the link between the variation under diffeomorphisms of the Einstein theory of gravitation and the Weyl anomaly of the conformal theory at infinity.Comment: LaTeX, 26 pages, 1 figure, modified version that will appear in Nucl. Phys.

The saddle-point method for condensed Bose gases

The application of the conventional saddle-point approximation to condensed Bose gases is thwarted by the approach of the saddle-point to the ground-state singularity of the grand canonical partition function. We develop and test a variant of the saddle-point method which takes proper care of this complication, and provides accurate, flexible, and computationally efficient access to both canonical and microcanonical statistics. Remarkably, the error committed when naively employing the conventional approximation in the condensate regime turns out to be universal, that is, independent of the system's single-particle spectrum. The new scheme is able to cover all temperatures, including the critical temperature interval that marks the onset of Bose--Einstein condensation, and reveals in analytical detail how this onset leads to sharp features in gases with a fixed number of particles. In particular, within the canonical ensemble the crossover from the high-temperature asymptotics to the condensate regime occurs in an error-function-like manner; this error function reduces to a step function when the particle number becomes large. Our saddle-point formulas for occupation numbers and their fluctuations, verified by numerical calculations, clearly bring out the special role played by the ground state.Comment: 32 pages, 11 figures. Ann. Phys. (N.Y.), in pres

Optimising text messaging to improve adherence to web-based smoking cessation treatment: a randomised control trial protocol

Introduction Millions of smokers use the Internet for smoking cessation assistance each year; however, most smokers engage minimally with even the best designed websites. The ubiquity of mobile devices and their effectiveness in promoting adherence in other areas of health behaviour change make them a promising tool to address adherence in Internet smoking cessation interventions. Text messaging is used by most adults, and messages can proactively encourage use of a web-based intervention. Text messaging can also be integrated with an Internet intervention to facilitate the use of core Internet intervention components. Methods and analysis We identified four aspects of a text message intervention that may enhance its effectiveness in promoting adherence to a web-based smoking cessation programme: personalisation, integration, dynamic tailoring and message intensity. Phase I will use a two-level full factorial design to test the impact of these four experimental features on adherence to a web-based intervention. The primary outcome is a composite metric of adherence that incorporates general utilisation metrics (eg, logins, page views) and specific feature utilisation shown to predict abstinence. Participants will be N=860 adult smokers who register on an established Internet cessation programme and enrol in its text message programme. Phase II will be a two-arm randomised trial to compare the efficacy of the web-based cessation programme alone and in conjunction with the optimised text messaging intervention on 30-day point prevalence abstinence at 9 months. Phase II participants will be N=600 adult smokers who register to use an established Internet cessation programme and enrol in text messaging. Secondary analyses will explore whether adherence mediates the effect of treatment condition on outcome. Ethics and dissemination This protocol was approved by Chesapeake IRB. We will disseminate study results through peer-reviewed manuscripts and conference presentations related to the methods and design, outcomes and exploratory analyses. Trial registration number NCT02585206

The Ursinus Weekly, November 4, 1976

Ursinus news in brief: S.F.A.R.C. approves letter; Ursinus to install new President; Schwalm invites students; Temple U. presents Brecht • Alarms, finance discussed • U.S.G.A. meets • Law professionals hosted • Comment: Why more trees? • Plant talk • Letter to the editor: Rules blasted • Photo concert • Bause files for patent • Marathon man • Harriers win one of three • Widener rips Bears • Hockey wins continue • Soccer loses twohttps://digitalcommons.ursinus.edu/weekly/1061/thumbnail.jp

Bandlimited approximations to the truncated Gaussian and applications

In this paper we extend the theory of optimal approximations of functions $f: \R \to \R$ in the $L^1(\R)$-metric by entire functions of prescribed exponential type (bandlimited functions). We solve this problem for the truncated and the odd Gaussians using explicit integral representations and fine properties of truncated theta functions obtained via the maximum principle for the heat operator. As applications, we recover most of the previously known examples in the literature and further extend the class of truncated and odd functions for which this extremal problem can be solved, by integration on the free parameter and the use of tempered distribution arguments. This is the counterpart of the work \cite{CLV}, where the case of even functions is treated.Comment: to appear in Const. Appro