dc.contributor.author |
Shami Nasr, Omar Bassam, |
dc.date.accessioned |
2017-08-30T14:29:17Z |
dc.date.available |
2017-08-30T14:29:17Z |
dc.date.issued |
2016 |
dc.date.submitted |
2016 |
dc.identifier.other |
b1869178x |
dc.identifier.uri |
http://hdl.handle.net/10938/11174 |
dc.description |
Thesis. M.S. American University of Beirut. Department of Mathematics, 2016. T:6402 |
dc.description |
Advisor : Dr. Raji, Wissam, Associate Professor, Mathematics ; Committee members : Dr. Abi- Khuzam, Faruk, Professor, Mathematics ; Dr. Khuri- Makdisi, Kamal, Professor, Mathematics. |
dc.description |
Includes bibliographical references (leaf 68) |
dc.description.abstract |
A modular form is a function meromorphic in the upper half plane and at the cusps. It satisfies certain transformation conditions under the full modular group The space of entire modular forms of integer weight on the full group is finite dimensional and thus the Fourier coefficients of these forms possess interesting arithmetical properties. Moreover, the zeroes of modular forms have been studied intensively and were the center of attention in the field. As an example, we show that the zeroes of the Eisenstein series of weight greater or equal to 4 lie on the portion of the unit circle. The (k+1) fold integral of a modular form gives rise to what is known as the period polynomials. These polynomials satisfy certain consistency condition and have interesting connections to L-functions. We show that the zeroes of period polynomials lie on the unit circle. |
dc.format.extent |
1 online resource (viii, 68 leaves) : color illustrations |
dc.language.iso |
eng |
dc.relation.ispartof |
Theses, Dissertations, and Projects |
dc.subject.classification |
T:006402 |
dc.subject.lcsh |
Polynomials. |
dc.subject.lcsh |
Holomorphic functions. |
dc.subject.lcsh |
Modular groups. |
dc.subject.lcsh |
Forms, Modular. |
dc.subject.lcsh |
Zero (The number) |
dc.title |
The zeroes of period polynomials - |
dc.type |
Thesis |
dc.contributor.department |
Faculty of Arts and Sciences. |
dc.contributor.department |
Department of Mathematics, |
dc.contributor.institution |
American University of Beirut. |