Monday 7th of November 2022, 14:00-15:00 in HG03.085
Berend Ringeling
Zeroes of Modular Forms.
"There are five elementary arithmetical operations: addition, subtraction, multiplication, division,
and... modular forms."-Eichler.
In this talk, we explore the magical world of modular forms. Modular forms are highly symmetric functions
on the complex upper half plane. One topic of interest is the zero location of these functions. For an
explicit family of these functions, the Eisenstein series, it is known that the zeros are located in a
very special region inside the complex upper half plane. Also for this family, the zeros over finite
fields are surprising, they are related to elliptic curves over finite fields with unusually large
endomorphism rings. We will discuss this family and, if time permits, other families of modular forms with
similar properties.