Some Modular Forms

Abstract

Bu çalışmada bazı modüler formlar incelenip T) ve 6 fonksiyonları yardımıyla bir çok ayrışım özdeşliği türetilmiştir.The theory of modular forms is one of the widest area of mathematics. It plays an essential role in Number Theory. In this study, we work out that Dedekind eta function, \eta a mock \theta function defined by a q-series convergent when q<1 and \eta_n,(n\in\Bbb{Z}) defined by the help of \eta are modular forms of half-integer weight on certain subgroups of SL_2(\Bbb{Z}). These functions appear in many identities of the partition theory. Some of them may be proved by a well-known theorem which will be stated in the text but, we don't present any of these proofs here. Therefore, for the use of this theorem we give complete identified sets of cusps of certain subgroups of SL_2(\Bbb{Z}) and the explicit formulas for the orders of these functions at various cusps.