Wednesday, November 29, 2017 - 2:15pm
William Paterson University
In this talk, I will discuss a family of functions deﬁned by Zagier in a very simple way as sums of powers of quadratic polynomials with integer coeﬃcients. Zagier showed that these functions have several surprising properties and are related many other subjects including modular forms, special values of zeta functions, Dio-phantine approximation and Dedekind sums. I will also discuss an extension of these functions to complex values using binary Hermitian forms and show that these functions also have similar properties as their real valued relatives.