A Modular Curve of Level 9 and the Class Number One Problem

In this note we give an explicit parametrization of the modular curve associated to the normalizer of a non-split Cartan subgroup of level 9. We determine all integral points of this modular curve. As an application, we give an alternative solution to the class number one problem.Comment: 18 page

The tame automorphism group in two variables over basic Artinian rings

In a recent paper it has been established that over an Artinian ring R all two-dimensional polynomial automorphisms having Jacobian determinant one are tame if R is a Q-algebra. This is a generalization of the famous Jung-Van der Kulk Theorem, which deals with the case that R is a field (of any characteristic). Here we will show that for tameness over an Artinian ring, the Q-algebra assumption is really needed: we will give, for local Artinian rings with square-zero principal maximal ideal, a complete description of the tame automorphism subgroup. This will lead to an example of a non-tame automorphism, for any characteristic p>0.Comment: 10 page

The role of modular functions in a class-number problem

The author has previously shown that there are exactly nine complex quadratic fields of class-number one. Here we show that the proof rests on some extremely interesting identities in modular functions which also provide a connection with the work of Heegner.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32990/1/0000374.pd

From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond

The discovery of connections between the distribution of energy levels of heavy nuclei and spacings between prime numbers has been one of the most surprising and fruitful observations in the twentieth century. The connection between the two areas was first observed through Montgomery's work on the pair correlation of zeros of the Riemann zeta function. As its generalizations and consequences have motivated much of the following work, and to this day remains one of the most important outstanding conjectures in the field, it occupies a central role in our discussion below. We describe some of the many techniques and results from the past sixty years, especially the important roles played by numerical and experimental investigations, that led to the discovery of the connections and progress towards understanding the behaviors. In our survey of these two areas, we describe the common mathematics that explains the remarkable universality. We conclude with some thoughts on what might lie ahead in the pair correlation of zeros of the zeta function, and other similar quantities.Comment: Version 1.1, 50 pages, 6 figures. To appear in "Open Problems in Mathematics", Editors John Nash and Michael Th. Rassias. arXiv admin note: text overlap with arXiv:0909.491

Geschlechtsbezogene Belästigung von Frauen am Arbeitsplatz

Geschlechtsbezogene Belästigung ist die Form von sexueller Belästigung mit der höchsten Prävalenz, dabei aber auch die empirisch am wenigsten untersuchte Form. Arbeitsumgebungen, in denen geschlechtsbezogene Belästigung einen Platz hat, bieten den Nährboden für sexualisierte Formen von sexueller Belästigung. Die Beforschung von geschlechtsbezogener Belästigung kann dazu beitragen, dieser in der Praxis entgegenzuwirken und folglich anderen Formen von sexueller Belästigung am Arbeitsplatz präventiv die Grundlage zu entziehen. Die vorliegende Studie untersucht deshalb die Prävalenz von geschlechtsbezogener Belästigung von Frauen am Arbeitsplatz im deutschsprachigen Raum, deren Bewältigung und die Rolle von ambivalent-sexistischen Einstellungen im Erleben und der Bewältigung des Phänomens. Hierfür wurde 757 berufstätigen Frauen eine Fragebogenbatterie online vorgegeben. Verwendet wurde eine deutsche Übersetzung des Gender Experiences Questionnaire (GEQ), eine deutsche Übersetzung und adaptierte Version des Coping with Harassment Questionnaire (CHQ) und die deutsche Version des Ambivalent Sexism Inventory (ASS). Im Schnitt waren Frauen gering und eher unregelmäßig von geschlechtsbezogener Belästigung betroffen, am stärksten von sexistischen Kommentaren und Infantilisierung. Es zeigten sich Branchen- und Altersunterschiede in der Betroffenheit und, dass Frauen die verschiedenen Facetten geschlechtsbezogener Belästigung als unterschiedlich unangenehm wahrnehmen. Die Bewältigung geschah mehrheitlich mittels internalen Bewältigungsstrategien und Vermeidungsverhalten, wobei erstere als am wenigsten effektiv und zweiteres als am effektivsten von allen untersuchten Bewältigungsstrategien wahrgenommen wurde. Während die hostil-sexistischen Einstellungen der Betroffenen gering negativ mit dem Ausmaß ihrer wahrgenommenen Betroffenheit und ihrem Einsatz von externalen Bewältigungsstrategien zusammenhingen, wurde für ihre benevolent-sexistischen Einstellungen ein gering positiver Zusammenhang mit beidem gefunden. Auf Basis der Ergebnisse werden Präventions- und Interventionsmaßnahmen für Organisationen diskutiert.Gender harassment is the subtype of sexual harassment with the highest prevalence, yet it is also the subtype that has been studied empirically the least. Work environments in which gender harassment happens are the basis for the occurrence of more severe, sexualized forms of sexual harassment. Research about gender harassment can be used to counteract its occurrence and consequently prevent the occurrence of the other forms of sexual harassment in the workplace. The present study therefore explores the prevalence of gender harassment targeting women at the workplace in German speaking countries, how women cope with such experiences, and the role of their own ambivalent sexist beliefs in their perception of gender harassment and in coping with it. Seven hundred fifty-seven working women were asked to fill out an online questionnaire, which included a German translation of the Gender Experiences Questionnaire (GEQ), an adapted version of the Coping with Harassment Questionnaire (CHQ), translated into German, and the German version of the Ambivalent Sexism Inventory (ASS). On average, women reported few and irregular experiences with gender harassment, with sexist comments and infantilization showing the highest prevalences. Further, differences in prevalence between various industries and between women of different age were found, as well as differences in how uncomfortable the different forms of gender harassment were perceived to be. Women used mainly internal coping strategies and avoidance behavior, the first being perceived to be the least and the second to be the most effective of all observed coping strategies. A low negative correlation between the women’s hostile-sexist beliefs and their perception of being targeted with gender harassment and their use of external coping strategies was found, respectively. For women’s benevolent-sexist beliefs, a low positive correlation with both variables was found. Finally, prevention and intervention measures for organizations are discussed