On Fields of rationality for automorphic representations

This paper proves two results on the field of rationality \Q(\pi) for an automorphic representation $\pi$, which is the subfield of \C fixed under the subgroup of \Aut(\C) stabilizing the isomorphism class of the finite part of $\pi$. For general linear groups and classical groups, our first main result is the finiteness of the set of discrete automorphic representations $\pi$ such that $\pi$ is unramified away from a fixed finite set of places, $\pi_\infty$ has a fixed infinitesimal character, and [\Q(\pi):\Q] is bounded. The second main result is that for classical groups, [\Q(\pi):\Q] grows to infinity in a family of automorphic representations in level aspect whose infinite components are discrete series in a fixed $L$-packet under mild conditions

Families of L-functions and their Symmetry

In [90] the first-named author gave a working definition of a family of automorphic L-functions. Since then there have been a number of works [33], [107], [67] [47], [66] and especially [98] by the second and third-named authors which make it possible to give a conjectural answer for the symmetry type of a family and in particular the universality class predicted in [64] for the distribution of the zeros near s=1/2. In this note we carry this out after introducing some basic invariants associated to a family

New q-Euler numbers and polynomials associated with p-adic q-integrals

In this paper we study q-Euler numbers and polynomials by using p-adic q-fermionic integrals on Z_p. The methods to study q-Euler numbers and polynomials in this paper are new.Comment: 13 page

Regional Financial Management Policy that Implies To Criminal Administration

Abstract: Regional autonomy can not be separated from the issue of the financial capacity of each region. In the previous year, autonomy is always associated with Automoney, it means that the independence of region in organizing its authority can be measured from its ability to explore the sources of income of its own. The Act No. 33 of 2004 is very concerning about the financial balance and accountability between the central government and the region in particular. This study used qualitative method, where data sources are obtained through field observation and literature study. The accountability and regional financial control and procedures for regional goverment budget are very important, because corruption seems to have been pervasive in all aspects of life, including in the government system. The linkage of administrative law with criminal law can be understood because both of them are a public law and in the process of law enforcement, criminal sanctions (criminal law) used to strengthen sanctions in state administrative law. In this case the criminal law is used to enforce the norms in other fields of law, or in other words functionalize the criminal law in the field of law.Keywords: Regional Autonomy, Accountability, Government, La

Active production of large aspheric optics for astronomy

This thesis is devoted mainly to tackling the unsolved problem of producing secondary mirrors for 8 m telescopes, which will be up to 2-2.5 m in diameter and in excess of 1000 waves aspheric. This cannot be done by traditional methods. The project directly addresses the problem and forms part of the UK's R and D contributions to the Gemini USA/UK/Canada/Brazil/Chile/Argentina project to produce two 8 m telescopes. Its aim was to develop a new active method. The thesis starts with a review of astronomical implications of 8 m telescope projects currently being undertaken or planned worldwide and continues with discussions on technological challenges specifically in main optics production. The first stage of producing the mirror is generation of the aspheric surface profile by diamond milling. This has been directly addressed by developing a new computer-controlled profiler based on the existing manual hardware of the Grubb-Parsons 2.5 m machine. An essential part of the development also includes a computer controlled contact profilometer. The system performance is presented, including calibration, error profile and convergence of error compensation. The main part of the project was to develop polishing using a full size active lap, by which the pressure distribution and hence ablation rate are modulated in real time. The progress of the project is described, starting with a review of other approaches being developed world wide. The overall philosophy and design of active components are presented. Following this, experiments with a sub-diameter polisher and a prototype active lap of 85 cm in diameter, as built, are also described, including methods of testing, ablation algorithm and control theory. The final part of this section discusses the performance of the active polishing lap in terms of functionality at component and system levels. The conclusion briefly summarises the evaluation of the active method and its impact on large optics production. It also gives ideas for future improvements of performance, research work still needed and viable applications for the technique

Supercuspidal part of the mod l cohomology of GU(1,n - 1)-Shimura varieties

Let l be a prime. In this paper we are concerned with GU(1,n - 1)-type Shimura varieties with arbitrary level structure at l and investigate the part of the cohomology on which G(ℚ[subscript p]) acts through mod l supercuspidal representations, where p ≠ l is any prime such that G(ℚ[subscript p]) is a general linear group. The main theorem establishes the mod l analogue of the local-global compatibility. Our theorem also encodes a global mod l Jacquet–Langlands correspondence in that the cohomology is described in terms of mod l automorphic forms on some compact inner form of G

Concept attainment in mathematics within content-based instruction for secondary English as a second language

The purpose of this project is to provide a useful model, the Concept Attainment Model in Mathematics, which implicates the concept attainment teaching method based on adjunct content-based instruction by using visuals and manipulatives in order to help ESL students be successful for both substantive content areas

COHOMOLOGY OF IGUSA CURVES -- A SURVEY (Automorphic forms, Automorphic representations, Galois representations, and its related topics)

We illustrate the strategy to compute the R-adic cohomology of Igusa varieties in the setup of ordinary modular curves, with updates on the literature towards a genrealization