In this paper we study the arithmetic properties of the ternary quadratic form $3x2 + 6y 2 + 14z 2 + 4yz + 2zx + 2xy$. This is the ternary quadratic form of least discriminant, which is conjectured, but has not been proven to be regular.

Material private information transmits through social networks. Using manually collected information on networks of alumni reunion cohorts, we show that hedge fund managers connected to directors of firms engaged in merger deals increase call option holdings on target firms before deal announcements. Effects are larger when reunion events for connected cohorts occur just before announcements. Independent directors, directors with short tenure, and directors with low stock ownership are more likely to transmit information. Our results are robust to confounding factors and alternative specifications. These findings highlight the role of social networks as channels of private information dissemination.

Recently Earnest and Haensch (2019) established that there are exactly twenty-nine (classes of) spinor regular primitive positive-definite integral ternary quadratic forms, which are not regular. In this paper we determine explicit formulas for the representation numbers of the twenty-seven of these ternary quadratic forms, which are alone in their spinor genus. For the remaining two spinor regular forms, which are not alone in their genus, we determine their representation numbers for even positive integers. As a consequence of our formulas we are able to determine exactly which positive integers are represented by the twenty-seven ternary quadratic forms alone in their spinor genus. The integers represented by six of these forms had been found by Lomadze in 1977 and three of them by Berkovich in 2015, one form of which had already been treated by Lomadze. Our method is a new approach and quite different from the methods of said authors.

We find that a significant proportion of the cross-sectional variation in the choice to own or rent is attributable to a genetic factor, while parental influence is not found to affect this choice. We also find evidence of gene-environment interactions: The environment moderates genetic effects on homeownership in that growing up in a wealthier family results in a stronger expression of genetic predispositions, while idiosyncratic life experiences appear to explain a larger portion of the variation in homeownership among those who grew up in a less wealthy family environment. Furthermore, we find that home location choices, for example, a familiar home location close to one’s birthplace and an urban versus a rural home location, are explained by both genetic factors and parental influence. Because we control for an extensive set of individual characteristics analyzed in existing research, an interpretation of our evidence is that an individual’s preferences with respect to homeownership and home location are partly genetic. The findings contribute to a deeper understanding of the factors that explain individual behavior with respect to the housing market, and add to an expanding literature on the biological and genetic factors that influence individuals’ economic and financial decisions.