Date of Degree

9-2016

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor(s)

Gautam Chinta

Committee Members

Carlos Moreno

Cormac O'Sullivan

Subject Categories

Number Theory

Keywords

binary hermitian forms, modular forms, continued fraction algorithms of complex numbers

Abstract

In one of his papers, Zagier defined a family of functions as sums of powers of quadratic polynomials. He showed that these functions have many surprising properties and are related to modular forms of integral weight and half integral weight, certain values of Dedekind zeta functions, Diophantine approximation, continued fractions, and Dedekind sums. He used the theory of periods of modular forms to explain the behavior of these functions. We study a similar family of functions, defining them using binary Hermitian forms. We show that this family of functions also have similar properties.

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