Let S2k(N) be the space of cusp forms of weight 2k and level N. Atkin-Lehner theory shows that S2k(N) can be decomposed into the oldspace and its orthogonal complement newspace. Again, from Atkin-Lehner theory, it follows that there exists a basis of newspace whose elements are simultaneous eigenforms of all the Hecke operators. Such eigenforms when normalized are called primitive forms. In 1932, Petersson introduced a harmonic weighted sum of the Fourier coefficients of an orthogonal basis B2k(N) for S2k(N), denoted by _2k;N . Petersson connected _2k;N to Kloosterman sums and Bessel functions, which is now known as the Petersson trace formula. The Petersson trace formula shows that _2k;N is independent of the choice of orthogonal basis. It is known that the oldspace decomposes into the images of newspaces of different levels under the scaling operator Bd where d is a proper divisor of N. It is of interest to derive a Petersson-type trace formula for primitive forms. In 2001, H. Iwaniec, W. Luo and P. Sarnak obtained an expression of Petersson-type trace formula for primitive forms in terms of _2k;N , when the level N is squarefree. Their method is to construct a special orthogonal basis for S2k(N). Using their approach, D. Rouymi has extended similar results to the case of prime power level in 2011. In this thesis, the case of arbitrary levels is investigated. Analogously, a special orthogonal basis is constructed and a Petersson-type trace formula for primitive forms in terms of _2k;N is found. The result established in this thesis recovers the results of H. Iwaniec, W. Luo and P. Sarnak, and D. Rouymi respectively for the cases of squarefree and prime power levels. / published_or_final_version / Mathematics / Master / Master of Philosophy

Thesis (Ph.D.)--University of Delaware, 2009. / Principal faculty advisor: Wenbo Li, Dept. of Mathematical Sciences. Includes bibliographical references.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 114-118). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 114-118). Also available on the Internet.

Orientador: David de Carvalho / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Agricola / Made available in DSpace on 2018-08-03T17:54:49Z (GMT). No. of bitstreams: 1 Ell_SandraMauren_M.pdf: 2752950 bytes, checksum: b0cef93a1b9f36cb20c63d765f8abcba (MD5) Previous issue date: 2003 / Mestrado

No description available.

We study the problem of the distribution of certain GL(3) Maass forms, namely, we obtain a Weyl’s law type result that characterizes the distribution of their eigenvalues, and an orthogonality relation for the Fourier coefficients of these Maass forms. The approach relies on a Kuznetsov trace formula on GL(3) and on the inversion formula for the Lebedev-Whittaker transform. The family of Maass forms being studied has zero density in the set of all GL(3) Maass forms and contains all self-dual forms. The self-dual forms on GL(3) can also be realised as symmetric square lifts of GL(2) Maass forms by the work of Gelbart-Jacquet. Furthermore, we also establish an explicit inversion formula for the Lebedev-Whittaker transform, in the nonarchimedean case, with a view to applications.

Let F be a local non-Archimedean field of characteristic zero. We prove a Plancherel formula for the symmetric space GL(2,F)\GL(2,E), where E/F is an unramified quadratic extension. Our method relies on intrinsic geometric and combinatorial properties of spherical varieties and constitutes the local counterpart of the global computation of the Flicker-Rallis period as a residue of periods against Eisenstein series. We also give a novel derivation of the Plancherel formula for the strongly tempered variety T\PGL(2) over F (with maximal split torus T) using a canonical smooth asymptotics morphism and a contour shifting method. In this rank one local setting, our proof is similar to Langlands' proof over global fields describing the spectrum of a reductive group in terms of residues of Eisenstein series. Finally, using both L2-decompositions, we develop a local relative trace formula and outline a comparison result in the setting of the unitary rank one Gan-Gross-Prasad conjecture.

<p>The research is based on the Financial crisis of the Historically Black Universities as well as the access problems encountered by students from poor backgrounds. Furthermore the research highlights the problems encountered by these students once they are accepted into these universities for example, the inability to cope withe the high standards of sudying at these institutions as well as the problem of paying their fees. the thesis shows the history of university funding in South Africa with emphasis on the differentfunding formulas, dating back to the era of the Holloway funding formula as well as the Van Wyk de Vries report, the SAPSE funding formula and different other mechanisms up to the present funding formula. Views of different educationalists will also be dealt with in regard to the funding problems of university education in South Africa.</p>

<p>The research is based on the Financial crisis of the Historically Black Universities as well as the access problems encountered by students from poor backgrounds. Furthermore the research highlights the problems encountered by these students once they are accepted into these universities for example, the inability to cope withe the high standards of sudying at these institutions as well as the problem of paying their fees. the thesis shows the history of university funding in South Africa with emphasis on the differentfunding formulas, dating back to the era of the Holloway funding formula as well as the Van Wyk de Vries report, the SAPSE funding formula and different other mechanisms up to the present funding formula. Views of different educationalists will also be dealt with in regard to the funding problems of university education in South Africa.</p>