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Philadelphia Area Number Theory Seminar

Wednesday, November 29, 2017 - 2:15pm

Cihan Karabulut

William Paterson University


Bryn Mawr College

Park Science Building, Room 337

Talk is scheduled to begin at 2:40 PM. Tea and refreshments will be served at 2:20 PM in Park Science Building, Room 339.

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.