00000ctm a22000004i 4500 UP-99796217613217944 Buklod 20200107114825.0 m |o d | ta 200107s2013 xx d r |||| u| (iLib)UPD-00429665696 DARCHIVES rda eng DMLUC LG 995 2013 M38 A756 Aricheta, Victor Manuel R. author. Hecke operators on the zeros of modular forms Victor Manuel R. Aricheta ; Fidel R. Nemenzo, adviser. Quezon City Institute of Mathematics, College of Science, University of the Philippines Diliman 2013. vii, 34 leaves illustrations 28 cm. text rdacontent unmediated rdamedia volume rdacarrier Thesis (M.S.- Mathematics) --University of the Philippines Diliman April 2013. Available to the general public. The first major result in locating the zeros of modular forms is due to Rankin and Swinnerton-Dyer who proved that all zeros of the Eisenstein series in the fundamental domain all lie on the unit circle. A modification of their approach led Getz to construct a family of modular forms with this same property. In here, we study the effect of the Hecke operators Tn to the zeros of modular forms. Following the construction of Getz, we provide a family of weight K modular forms for which the zeros of Tnf in the fundamental domain all lie on the unit circle.Then, we investigate the relationship between the zeros of a modular form f and Tnf. We prove that if Tn has distinct eigenvalues, then f and Tnf have precisely the same zeros if and only if f is an eigenform. As a consequence, for weights less than or equal to 24, we give the form of f depending on the number of zeros shared by f and Tnf. Hecke operators. Forms, Modular. Nemenzo, Fidel R. author. FI UPD DARCHIVES LG 995 2013 M38 A756 Thesis