Event Detail

Event Type: 
Wednesday, May 30, 2018 - 14:00 to 16:00
Valley Library Room: 1420

In this dissertation, we begin by presenting the result of F. K. C. Rankin and Swinnerton-Dyer on the location of the zeros of the Eisenstein series for the full modular group in the standard fundamental domain. Their simple but beautiful argument shows that all zeros are located on the lower boundary arc of the fundamental domain.

Then, we introduce families of certain combinations of products of Eisenstein series and explore the location of their zeros in the fundamental domain. By extending F.K.C. Rankin and Swinnerton-Dyer argument, we show that almost all modular forms in our families have property that many of their zeros in the fundamental domain lie on the boundary of the fundamental domain.