Further refinement of strong multiplicity one for GL(2)

We obtain a sharp refinement of the strong multiplicity one theorem for the case of unitary non-dihedral cuspidal automorphic representations for GL(2). Given two unitary cuspidal automorphic representations for GL(2) that are not twist-equivalent, we also find sharp lower bounds for the number of places where the Hecke eigenvalues are not equal, for both the general and non-dihedral cases. We then construct examples to demonstrate that these results are sharp.Comment: 21 pages. To appear in Transactions of the American Mathematical Societ

On the size of Satake parameters for unitary cuspidal automorphic representations for GL(4)

Let \Pi\ be a cuspidal automorphic representation for GL(4) over a number field F. We obtain unconditional lower bounds on the number of places at which the Satake parameters are not "too large". In the case of self-dual \Pi\ with non-trivial central character, our results imply that the set of places at which \Pi\ is tempered has an explicit positive lower Dirichlet density. Our methods extend those of Ramakrishnan by careful analysis of the hypothetical possibilities for the structure of the Langlands conjugacy classes, as well as their behaviour under functorial lifts. We then discuss the analogous problem in GL(3).Comment: 15 page

The 2 Rs – respect and responsibility: the case of Australian Muslim girls

The citizenship debate involves respect and responsibility, and these can be achieved through collective action. Though many members of disadvantaged groups sympathise with the goals of social movements fighting injustice against their in-group (own community) or out-group (wider society) often only a small percentage of them actually participate in collective activities staged to realise these goals. In this paper I discuss the case of Australian Muslims girls who in their home environment respect the family values and carry out certain responsibilities assigned to them. By family values, I mean respect for elders, performing religious duties, for example, offering prayers, and fasting during the month of Ramadan, helping mother in the kitchen and looking after their siblings. In the wider society, Muslim girls attend schools, do part-time jobs and obey Australian values of fair-go, tolerance and multiculturalism ceremoniousl. However, I question in this paper, whether their family and the wider society are working collectively to fulfil their responsibility towards these girls. I discuss the interview responses of 39 Muslim girls (15-18 years) living in Sydney and Perth. I examine pertinent cases within the framework of relevant academic literature, and argue within the social, religious and cultural context. The issues within the family domain are inter-twined within Islamic religious-cultural arguments, whereas the issues in the public domain are argued on cultural conflict between the Muslims and the wider society. With both arguments I show how some Muslim girls negotiate their identity, and suggest their bicultural identity is assisting them to keep a positive attitude in their everyday life. Finally, I advocate that collective action from both the Muslim and the wider community is vital for the well-being of these girls.   Cosmopolitan Civil Societies Journal, Vol.1, No.3, 200