Revisiting The Riemann Zeta Function at Positive Even Integers

Using Parseval's identity for the Fourier coefficients of $x^k$, we provide a new proof that $\zeta(2k)=\dfrac{(-1)^{k+1}B_{2k}(2\pi)^{2k}}{2(2k)!}$.Comment: 6 pages, no figure

A new four parameter q-series identity and its partition implications

We prove a new four parameter q-hypergeometric series identity from which the three parameter key identity for the Goellnitz theorem due to Alladi, Andrews, and Gordon, follows as a special case by setting one of the parameters equal to 0. The new identity is equivalent to a four parameter partition theorem which extends the deep theorem of Goellnitz and thereby settles a problem raised by Andrews thirty years ago. Some consequences including a quadruple product extension of Jacobi's triple product identity, and prospects of future research are briefly discussed.Comment: 25 pages, in Sec. 3 Table 1 is added, discussion is added at the end of Sec. 5, minor stylistic changes, typos eliminated. To appear in Inventiones Mathematica

An Economic Analysis of a Drug-Selling Gang's Finances

We analyze a unique data set detailing the financial activities of a drug-selling street gang on a monthly basis over a four-year period in the recent past. The data, originally compiled by the gang leader to aid in managing the organization, contain detailed information on both the sources of revenues (e.g. drug sales, extortion) and expenditrues (e.g. costs of drugs sold, weapons, tribute to the central gang organization, wages paid to various levels of the gang). Street-level drug dealing appears to be less lucrative than is generally though. We estimate the average wage in the organization to rise from roughly $6 per hour to$11 per hour over the time period studied. The distribution of wages, however, is extremely skewed. Gang leaders earn far more than they could in the legitimate sector, but the actual street-level dealers appear to earn less than the minimum wage throughout most of our sample, in spite of the substantial risks associated with such activities (the annual violent death rate in our sample is 0.07), There is some evidence consistent both with compensating differentials and efficiency wages. The markup on drugs suggests that the gang has substantial local market power. Gang wars appear to have an important strategic component: violence on another gang's turf shifts demand away from that area. The gang we observe responds to such attacks by pricing below marginal cost, suggesting either economic punishment for the rival gang or the presence of switching for users that makes market share maintenance valuable. We investigate a range of alternative methods for estimating the willingness of gang members to accept risks of death, all of which suggest that the implicit value that gang members place on their own lives is very low.

Experience-Based Design: Some Concepts and Issues

Recently, marketing scholars have emphasized the importance of orchestrating memorable consumer experiences. Product design is a central element of engineering compelling consumer experience. This has resulted in the emergence of experience design as a theoretically significant area of study in disciplines such as design theory. Within marketing there is inadequate research on building theoretical frameworks that explicitly focus on integrating experience design into product development. To address this gap, this paper proposes a conceptual model of new product development that is embedded in an experience-based design approach. The paper contributes by extending current understanding and highlighting future research directions in the domain of new product development

Women over 40, foreigners of color, and other missing persons in globalizing mediascapes: understanding marketing images as mirrors of intersectionality

Media diversity studies regularly invoke the notion of marketing images as mirrors of racism and sexism. This article develops a higher-order concept of marketing images as “mirrors of intersectionality.” Drawing on a seven-dimensional study of coverperson diversity in a globalizing mediascape, the emergent concept highlights that marketing images reflect not just racism and sexism, but all categorical forms of marginalization, including ableism, ageism, colorism, fatism, and heterosexism, as well as intersectional forms of marginalization, such as sexist ageism and racist multiculturalism. Fueled by the legacies of history, aspirational marketing logics, and an industry-wide distribution of discriminatory work, marketing images help to perpetuate multiple, cumulative, and enduring advantages for privileged groups and disadvantages for marginalized groups. In this sense, marketing images, as mirrors of intersectionality, are complicit agents in the structuration of inequitable societies