Construction of modular forms with Poincaré series
Date
2010
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Yeşilyurt, Hamza
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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.
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Degree Discipline
Mathematics
Degree Level
Master's
Degree Name
MS (Master of Science)
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Language
English