The Fourier coefficients of Siegel modular forms of degree two
Saldana, Rudolph Lolo
Resnikoff, H. L.
Master of Arts
In this thesis, two conjectures concerning the Fourier coefficients of Siegel modular forms of degree two are presented. From these two conjectures, which have a certain "naturality" and simplicity within the framework of known results, are derived formulae which completely determine the generator of the graded ring of modular forms of even weight through its Fourier coefficients. Additionally, to add credence to the conjectures, one of three known methods of generating Fourier coefficients of modular forms is used to obtain a table of coefficients with which to illustrate the conjectures. It may be mentioned that this set of Fourier coefficients, in itself, represents the first known table of any length for the Siegel modular forms of degree two.