Dissertations, Theses, and Capstone Projects
Date of Degree
9-2016
Document Type
Dissertation
Degree Name
Ph.D.
Program
Mathematics
Advisor
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.
Recommended Citation
Karabulut, Cihan, "On Sums of Binary Hermitian Forms" (2016). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/1556