Construction of modular forms with Poincaré series

Date

2010

Editor(s)

Advisor

Yeşilyurt, Hamza

Supervisor

Co-Advisor

Co-Supervisor

Instructor

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Abstract

In this thesis, we construct holomorphic modular forms of integral weight k > 2 for the principle congruence subgroup Γ( ¯ N) by means of Poincar´e series. We start by providing the necessary background information on modular forms. Then, we show that Poincar´e series are in fact holomorphic modular forms and we obtain explicit formulas for their Fourier coefficients. For the special case when Poincar´e series are Eisenstein series, their Fourier coefficients become relatively simple. We give Fourier coefficients of the Eisenstein series belonging to the principle congruence subgroup. Finally, as an application of what has been studied, we construct Eisenstein series for the Hecke congruence supgroup.

Source Title

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Course

Other identifiers

Book Title

Degree Discipline

Mathematics

Degree Level

Master's

Degree Name

MS (Master of Science)

Citation

Published Version (Please cite this version)

Language

English

Type