Calculating all elements of minimal index in the infinite parametric family of simplest quartic fields

summary:It is a classical problem in algebraic number theory to decide if a number field is monogeneous, that is if it admits power integral bases. It is especially interesting to consider this question in an infinite parametric family of number fields. In this paper we consider the infinite parametric family of simplest quartic fields $K$ generated by a root $\xi$ of the polynomial $P_t(x)=x^4-tx^3-6x^2+tx+1$, assuming that $t>0$, $t\neq 3$ and $t^2+16$ has no odd square factors. In addition to generators of power integral bases we also calculate the minimal index and all elements of minimal index in all fields in this family

30 years of collaboration

We highlight some of the most important cornerstones of the long standing and very fruitful collaboration of the Austrian Diophantine Number Theory research group and the Number Theory and Cryptography School of Debrecen. However, we do not plan to be complete in any sense but give some interesting data and selected results that we find particularly nice. At the end we focus on two topics in more details, namely a problem that origins from a conjecture of Rényi and Erdős (on the number of terms of the square of a polynomial) and another one that origins from a question of Zelinsky (on the unit sum number problem). This paper evolved from a plenary invited talk that the authors gaveat the Joint Austrian-Hungarian Mathematical Conference 2015, August 25-27, 2015 in Győr (Hungary)

The politics of performance: transnationalism and its limits in former Yugoslav popular music, 1999–2004

This paper examines transnational relations between the Yugoslav successor states from the point of view of popular music, and demonstrates how transnational musical figures (such as Djordje Balaševi?, Mom?ilo Bajagi?-Bajaga and Ceca Ražnatovi?) are interpreted as symbolic reference points in national ethnopolitical discourse in the process of identity construction. Another symbolic function is served by Serbian turbofolk artists, who in Croatia serve as a cultural resource to distance oneself from a musical genre associated by many urban Croats with the ruralization (and Herzegovinization) of Croatian city space. In addition, value judgements associated with both Serbian and Croatian newly composed folk music provide an insight into the transnational negotiation of conflicting identities in the ex-Yugoslav context. Ultimately the paper shows how the ethnonational boundaries established by nationalizing ideologies created separate cultural spaces which themselves have been transnationalized after Yugoslavia's disintegration